lib/examples/instant_preview.lyx

   1 #LyX 2.0.0svn created this file. For more info see http://www.lyx.org/
   2 \lyxformat 385
   3 \begin_document
   4 \begin_header
   5 \textclass article
   6 \begin_preamble
   7 \usepackage[all, knot]{xy}
   8 \xyoption{arc}
   9 \usepackage{qtree}
  10 \usepackage{tipa}
  11 \end_preamble
  12 \use_default_options false
  13 \maintain_unincluded_children false
  14 \language english
  15 \inputencoding auto
  16 \fontencoding global
  17 \font_roman lmodern
  18 \font_sans default
  19 \font_typewriter default
  20 \font_default_family default
  21 \use_xetex false
  22 \font_sc false
  23 \font_osf false
  24 \font_sf_scale 100
  25 \font_tt_scale 100
  26
  27 \graphics default
  28 \default_output_format default
  29 \bibtex_command default
  30 \index_command default
  31 \paperfontsize default
  32 \spacing single
  33 \use_hyperref false
  34 \papersize default
  35 \use_geometry false
  36 \use_amsmath 1
  37 \use_esint 1
  38 \use_mhchem 1
  39 \cite_engine basic
  40 \use_bibtopic false
  41 \use_indices false
  42 \paperorientation portrait
  43 \suppress_date false
  44 \index Index
  45 \shortcut idx
  46 \color #008000
  47 \end_index
  48 \secnumdepth 3
  49 \tocdepth 3
  50 \paragraph_separation indent
  51 \paragraph_indentation default
  52 \quotes_language english
  53 \papercolumns 1
  54 \papersides 1
  55 \paperpagestyle default
  56 \tracking_changes false
  57 \output_changes false
  58 \html_math_output 0
  59 \html_be_strict true
  60 \end_header
  61
  62 \begin_body
  63
  64 \begin_layout Section
  65 Introduction
  66 \end_layout
  67
  68 \begin_layout Standard
  69 The following packages are needed to be installed at your computer in order
  70  to typeset the document properly and have instant preview working:
  71 \end_layout
  72
  73 \begin_layout LyX-Code
  74 xy.sty, qtree.sty, tipa.sty
  75 \end_layout
  76
  77 \begin_layout Section
  78 Diagrams by XY(-pic)
  79 \end_layout
  80
  81 \begin_layout Standard
  82 Few examples of diagrams were taken from Aaron Landa's archive of xy-pic
  83  examples, see
  84 \begin_inset Flex URL
  85 status collapsed
  86
  87 \begin_layout Plain Layout
  88
  89 http://www.math.columbia.edu/~lauda/xy/
  90 \end_layout
  91
  92 \end_inset
  93
  94 .
  95 \end_layout
  96
  97 \begin_layout Description
  98 Braid
  99 \end_layout
 100
 101 \begin_layout Standard
 102 \begin_inset Preview
 103
 104 \begin_layout Standard
 105 \begin_inset ERT
 106 status collapsed
 107
 108 \begin_layout Plain Layout
 109
 110
 111 \backslash
 112 xy
 113 \end_layout
 114
 115 \begin_layout Plain Layout
 116
 117 (5,10)*{}; (-10,-10)*{} **
 118 \backslash
 119 crv{(6,-2)&(-12,4)}
 120 \end_layout
 121
 122 \begin_layout Plain Layout
 123
 124
 125 \backslash
 126 POS?(.25)*{
 127 \backslash
 128 hole}="x"
 129 \backslash
 130 POS?(.45)*{
 131 \backslash
 132 hole}="y"
 133 \backslash
 134 POS?(.6)*{
 135 \backslash
 136 hole}="z";
 137 \end_layout
 138
 139 \begin_layout Plain Layout
 140
 141 "y"+(0,-1); (2,-10)*{} **
 142 \backslash
 143 crv{}
 144 \backslash
 145 POS?(.2)*{
 146 \backslash
 147 hole}="M";
 148 \end_layout
 149
 150 \begin_layout Plain Layout
 151
 152 (-10,10)*{}; "z" **
 153 \backslash
 154 crv{(-9,0)};
 155 \end_layout
 156
 157 \begin_layout Plain Layout
 158
 159 "z"; "M" **
 160 \backslash
 161 crv{};
 162 \end_layout
 163
 164 \begin_layout Plain Layout
 165
 166 "M"; "x" **
 167 \backslash
 168 crv{(5,0)};
 169 \end_layout
 170
 171 \begin_layout Plain Layout
 172
 173 "x"; "y" **
 174 \backslash
 175 crv{(0,7) & (-5,6)};
 176 \end_layout
 177
 178 \begin_layout Plain Layout
 179
 180
 181 \backslash
 182 endxy
 183 \end_layout
 184
 185 \end_inset
 186
 187
 188 \end_layout
 189
 190 \end_inset
 191
 192
 193 \end_layout
 194
 195 \begin_layout Description
 196 Knots
 197 \end_layout
 198
 199 \begin_layout Standard
 200 \begin_inset Preview
 201
 202 \begin_layout Standard
 203 \begin_inset ERT
 204 status collapsed
 205
 206 \begin_layout Plain Layout
 207
 208
 209 \backslash
 210 xy
 211 \end_layout
 212
 213 \begin_layout Plain Layout
 214
 215 (6,9)*{}="1";
 216 \end_layout
 217
 218 \begin_layout Plain Layout
 219
 220 (-8.5,-1)*{}="2";
 221 \end_layout
 222
 223 \begin_layout Plain Layout
 224
 225 "1";"2" **
 226 \backslash
 227 crv{~*=<.5pt>{.} (0,30)}?(.75)*
 228 \backslash
 229 dir{>}+(-2,2)*{z};
 230 \end_layout
 231
 232 \begin_layout Plain Layout
 233
 234 (-6.5,8)*{}="1";
 235 \end_layout
 236
 237 \begin_layout Plain Layout
 238
 239 (-.5,-9)*{}="2";
 240 \end_layout
 241
 242 \begin_layout Plain Layout
 243
 244 "1";"2" **
 245 \backslash
 246 crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
 247 \backslash
 248 dir{>}+(-2,-2)*{u};
 249 \end_layout
 250
 251 \begin_layout Plain Layout
 252
 253 (-9.5,-3.35)*{}="1";
 254 \end_layout
 255
 256 \begin_layout Plain Layout
 257
 258 (8.5,-3)*{}="2";
 259 \end_layout
 260
 261 \begin_layout Plain Layout
 262
 263 "1";"2" **
 264 \backslash
 265 crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)*
 266 \backslash
 267 dir{>}+(-1,-3)*{x};
 268 \end_layout
 269
 270 \begin_layout Plain Layout
 271
 272 (1,-10)*{}="1";
 273 \end_layout
 274
 275 \begin_layout Plain Layout
 276
 277 (6.5,7.13)*{}="2";
 278 \end_layout
 279
 280 \begin_layout Plain Layout
 281
 282 "1";"2" **
 283 \backslash
 284 crv{~*=<.5pt>{.} (17.67,-24.19)}?(.7)*
 285 \backslash
 286 dir{>}+(3,-1)*{y};
 287 \end_layout
 288
 289 \begin_layout Plain Layout
 290
 291 (11,-1)*{}="1";
 292 \end_layout
 293
 294 \begin_layout Plain Layout
 295
 296 (-4,8)*{}="2";
 297 \end_layout
 298
 299 \begin_layout Plain Layout
 300
 301 "1";"2" **
 302 \backslash
 303 crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
 304 \backslash
 305 dir{>}+(1,2)*{w};
 306 \end_layout
 307
 308 \begin_layout Plain Layout
 309
 310
 311 \backslash
 312 endxy
 313 \end_layout
 314
 315 \end_inset
 316
 317
 318 \end_layout
 319
 320 \end_inset
 321
 322
 323 \end_layout
 324
 325 \begin_layout Description
 326 Circles
 327 \end_layout
 328
 329 \begin_layout Standard
 330 \begin_inset Preview
 331
 332 \begin_layout Standard
 333 \begin_inset ERT
 334 status collapsed
 335
 336 \begin_layout Plain Layout
 337
 338
 339 \backslash
 340 xy
 341 \end_layout
 342
 343 \begin_layout Plain Layout
 344
 345 (0,0)*
 346 \backslash
 347 xycircle(14,8){++
 348 \backslash
 349 dir{<}};
 350 \end_layout
 351
 352 \begin_layout Plain Layout
 353
 354 (0,0)*
 355 \backslash
 356 xycircle<10pt>{{.}};
 357 \end_layout
 358
 359 \begin_layout Plain Layout
 360
 361 (0,0)*
 362 \backslash
 363 xycircle(5,2){:};
 364 \end_layout
 365
 366 \begin_layout Plain Layout
 367
 368 (0,15)*
 369 \backslash
 370 xycircle(10,4){--};
 371 \end_layout
 372
 373 \begin_layout Plain Layout
 374
 375
 376 \backslash
 377 endxy
 378 \end_layout
 379
 380 \end_inset
 381
 382
 383 \end_layout
 384
 385 \end_inset
 386
 387
 388 \end_layout
 389
 390 \begin_layout Description
 391 Cobordism
 392 \end_layout
 393
 394 \begin_layout Standard
 395 \begin_inset Preview
 396
 397 \begin_layout Standard
 398 \begin_inset ERT
 399 status collapsed
 400
 401 \begin_layout Plain Layout
 402
 403
 404 \backslash
 405 xy
 406 \end_layout
 407
 408 \begin_layout Plain Layout
 409
 410 (0,0)*
 411 \backslash
 412 ellipse(3,1){.};
 413 \end_layout
 414
 415 \begin_layout Plain Layout
 416
 417 (0,0)*
 418 \backslash
 419 ellipse(3,1)__,=:a(-180){-};
 420 \end_layout
 421
 422 \begin_layout Plain Layout
 423
 424 (-6,-8)*
 425 \backslash
 426 ellipse(3,1){.};
 427 \end_layout
 428
 429 \begin_layout Plain Layout
 430
 431 (6,-8)*
 432 \backslash
 433 ellipse(3,1){.};
 434 \end_layout
 435
 436 \begin_layout Plain Layout
 437
 438 (0,-8)*
 439 \backslash
 440 ellipse(3,1){.};
 441 \end_layout
 442
 443 \begin_layout Plain Layout
 444
 445 (-6,-8)*
 446 \backslash
 447 ellipse(3,1)__,=:a(-180){-};
 448 \end_layout
 449
 450 \begin_layout Plain Layout
 451
 452 (6,-8)*
 453 \backslash
 454 ellipse(3,1)__,=:a(-180){-};
 455 \end_layout
 456
 457 \begin_layout Plain Layout
 458
 459 (0,-8)*
 460 \backslash
 461 ellipse(3,1)__,=:a(180){-};
 462 \end_layout
 463
 464 \begin_layout Plain Layout
 465
 466 (-3,6)*
 467 \backslash
 468 ellipse(3,1){-};
 469 \end_layout
 470
 471 \begin_layout Plain Layout
 472
 473 (3,6)*
 474 \backslash
 475 ellipse(3,1){-};
 476 \end_layout
 477
 478 \begin_layout Plain Layout
 479
 480 (-3,12)*{}="1";
 481 \end_layout
 482
 483 \begin_layout Plain Layout
 484
 485 (3,12)*{}="2";
 486 \end_layout
 487
 488 \begin_layout Plain Layout
 489
 490 (-9,12)*{}="A2";
 491 \end_layout
 492
 493 \begin_layout Plain Layout
 494
 495 (9,12)*{}="B2";
 496 \end_layout
 497
 498 \begin_layout Plain Layout
 499
 500 "1";"2" **
 501 \backslash
 502 crv{(-3,7) & (3,7)};
 503 \end_layout
 504
 505 \begin_layout Plain Layout
 506
 507 (-3,0)*{}="A";
 508 \end_layout
 509
 510 \begin_layout Plain Layout
 511
 512 (3,0)*{}="B";
 513 \end_layout
 514
 515 \begin_layout Plain Layout
 516
 517 (-3,1)*{}="A1";
 518 \end_layout
 519
 520 \begin_layout Plain Layout
 521
 522 (3,1)*{}="B1";
 523 \end_layout
 524
 525 \begin_layout Plain Layout
 526
 527 "A";"A1" **
 528 \backslash
 529 dir{-};
 530 \end_layout
 531
 532 \begin_layout Plain Layout
 533
 534 "B";"B1" **
 535 \backslash
 536 dir{-};
 537 \end_layout
 538
 539 \begin_layout Plain Layout
 540
 541 "B2";"B1" **
 542 \backslash
 543 crv{(8,7) & (3,5)};
 544 \end_layout
 545
 546 \begin_layout Plain Layout
 547
 548 "A2";"A1" **
 549 \backslash
 550 crv{(-8,7) & (-3,5)};
 551 \end_layout
 552
 553 \begin_layout Plain Layout
 554
 555 %REFLECT
 556 \end_layout
 557
 558 \begin_layout Plain Layout
 559
 560 (3,-16)*{}="1";
 561 \end_layout
 562
 563 \begin_layout Plain Layout
 564
 565 (9,-16)*{}="2";
 566 \end_layout
 567
 568 \begin_layout Plain Layout
 569
 570 "1";"2" **
 571 \backslash
 572 crv{(3,-10) & (9,-10)};
 573 \end_layout
 574
 575 \begin_layout Plain Layout
 576
 577 (-3,-16)*{}="1";
 578 \end_layout
 579
 580 \begin_layout Plain Layout
 581
 582 (-9,-16)*{}="2";
 583 \end_layout
 584
 585 \begin_layout Plain Layout
 586
 587 "1";"2" **
 588 \backslash
 589 crv{(-3,-10) & (-9,-10)};
 590 \end_layout
 591
 592 \begin_layout Plain Layout
 593
 594 (-15,-16)*{}="A2";
 595 \end_layout
 596
 597 \begin_layout Plain Layout
 598
 599 (15,-16)*{}="B2";
 600 \end_layout
 601
 602 \begin_layout Plain Layout
 603
 604 (-3,0)*{}="A";
 605 \end_layout
 606
 607 \begin_layout Plain Layout
 608
 609 (3,0)*{}="B";
 610 \end_layout
 611
 612 \begin_layout Plain Layout
 613
 614 (-3,-1)*{}="A1";
 615 \end_layout
 616
 617 \begin_layout Plain Layout
 618
 619 (3,-1)*{}="B1";
 620 \end_layout
 621
 622 \begin_layout Plain Layout
 623
 624 "A";"A1" **
 625 \backslash
 626 dir{-};
 627 \end_layout
 628
 629 \begin_layout Plain Layout
 630
 631 "B";"B1" **
 632 \backslash
 633 dir{-};
 634 \end_layout
 635
 636 \begin_layout Plain Layout
 637
 638 "B2";"B1" **
 639 \backslash
 640 crv{(13,-6) & (2,-8)};
 641 \end_layout
 642
 643 \begin_layout Plain Layout
 644
 645 "A2";"A1" **
 646 \backslash
 647 crv{(-13,-6) & (-2,-8)};
 648 \end_layout
 649
 650 \begin_layout Plain Layout
 651
 652
 653 \backslash
 654 endxy
 655 \end_layout
 656
 657 \end_inset
 658
 659
 660 \end_layout
 661
 662 \end_inset
 663
 664
 665 \begin_inset Preview
 666
 667 \begin_layout Standard
 668 \begin_inset ERT
 669 status collapsed
 670
 671 \begin_layout Plain Layout
 672
 673
 674 \backslash
 675 xy 0;/r.18pc/:
 676 \end_layout
 677
 678 \begin_layout Plain Layout
 679
 680 (20,2)*{
 681 \backslash
 682 bullet}="RU"+(1,3)*{x^{
 683 \backslash
 684 ast}};
 685 \end_layout
 686
 687 \begin_layout Plain Layout
 688
 689 (16,-3)*{
 690 \backslash
 691 bullet}="RD"+(2.5,2)*{x^{
 692 \backslash
 693 ast}};
 694 \end_layout
 695
 696 \begin_layout Plain Layout
 697
 698 (-16,2)*{
 699 \backslash
 700 bullet}="LU"+(-1,2)*{x};
 701 \end_layout
 702
 703 \begin_layout Plain Layout
 704
 705 (-20,-3)*{
 706 \backslash
 707 bullet}="LD"+(-1,2)*{x};
 708 \end_layout
 709
 710 \begin_layout Plain Layout
 711
 712 "RU";"RD" **
 713 \backslash
 714 crv{(4,2) & (4,-1)}; ?(.1)*
 715 \backslash
 716 dir{<}; ?(.85)*
 717 \backslash
 718 dir{<};
 719 \end_layout
 720
 721 \begin_layout Plain Layout
 722
 723 "LD";"LU" **
 724 \backslash
 725 crv{(-4,-2) & (-4,1)};
 726 \end_layout
 727
 728 \begin_layout Plain Layout
 729
 730 ?(.08)*
 731 \backslash
 732 dir{<}; ?(.85)*
 733 \backslash
 734 dir{<};
 735 \end_layout
 736
 737 \begin_layout Plain Layout
 738
 739 (7.5,0)*{}="x1"; (-7.5,0)*{}="x2";
 740 \end_layout
 741
 742 \begin_layout Plain Layout
 743
 744 "x1"; "x2" **
 745 \backslash
 746 crv{(7,-10) & (-7,-10)};
 747 \end_layout
 748
 749 \begin_layout Plain Layout
 750
 751 (16,-20)*{
 752 \backslash
 753 bullet}="RDD"+(2.5,-1)*{x^{
 754 \backslash
 755 ast}};
 756 \end_layout
 757
 758 \begin_layout Plain Layout
 759
 760 (-20,-20)*{
 761 \backslash
 762 bullet}="LDD"+(-1,-3)*{x};
 763 \end_layout
 764
 765 \begin_layout Plain Layout
 766
 767 (20,-12.5)*{
 768 \backslash
 769 bullet}="RUD"+(3.5,1)*{x^{
 770 \backslash
 771 ast}};
 772 \end_layout
 773
 774 \begin_layout Plain Layout
 775
 776 (-16,-15)*{
 777 \backslash
 778 bullet}="LUD";
 779 \end_layout
 780
 781 \begin_layout Plain Layout
 782
 783 (-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B";
 784 \end_layout
 785
 786 \begin_layout Plain Layout
 787
 788 "RD"; "RDD" **
 789 \backslash
 790 dir{-};
 791 \end_layout
 792
 793 \begin_layout Plain Layout
 794
 795 "LD"; "LDD" **
 796 \backslash
 797 dir{-};
 798 \end_layout
 799
 800 \begin_layout Plain Layout
 801
 802 "A"; "LUD" **
 803 \backslash
 804 dir{.};
 805 \end_layout
 806
 807 \begin_layout Plain Layout
 808
 809 "RDD"; "LDD" **
 810 \backslash
 811 crv{(0,-17)}; ?(.57)*
 812 \backslash
 813 dir{>};
 814 \end_layout
 815
 816 \begin_layout Plain Layout
 817
 818 "RU"; "RUD" **
 819 \backslash
 820 dir{-};
 821 \end_layout
 822
 823 \begin_layout Plain Layout
 824
 825 "LU"; "A" **
 826 \backslash
 827 dir{-};
 828 \end_layout
 829
 830 \begin_layout Plain Layout
 831
 832 "B"; "RUD" **
 833 \backslash
 834 crv{(18,-14.15)};
 835 \end_layout
 836
 837 \begin_layout Plain Layout
 838
 839 "B"; "LUD" **
 840 \backslash
 841 crv{~*=<4pt>{.}(0,-18)}; ?(.4)*
 842 \backslash
 843 dir{<};
 844 \end_layout
 845
 846 \begin_layout Plain Layout
 847
 848
 849 \backslash
 850 endxy
 851 \end_layout
 852
 853 \end_inset
 854
 855
 856 \end_layout
 857
 858 \end_inset
 859
 860
 861 \end_layout
 862
 863 \begin_layout Description
 864 Strings
 865 \end_layout
 866
 867 \begin_layout Standard
 868 \begin_inset Preview
 869
 870 \begin_layout Standard
 871 \begin_inset ERT
 872 status open
 873
 874 \begin_layout Plain Layout
 875
 876
 877 \backslash
 878 xy (-15,0)*{};(15,0)*{};
 879 \end_layout
 880
 881 \begin_layout Plain Layout
 882
 883
 884 \backslash
 885 endxy
 886 \end_layout
 887
 888 \begin_layout Plain Layout
 889
 890
 891 \backslash
 892 qquad =
 893 \backslash
 894 qquad
 895 \backslash
 896 xy
 897 \end_layout
 898
 899 \begin_layout Plain Layout
 900
 901 (-10,12)*{}; (-10,-12)*{}; **
 902 \backslash
 903 dir{-}?(.5)*
 904 \backslash
 905 dir{<}+(-4,0)*{F(x)};
 906 \end_layout
 907
 908 \begin_layout Plain Layout
 909
 910 (-2,12)*{}="1";
 911 \end_layout
 912
 913 \begin_layout Plain Layout
 914
 915 (6,-7) *{}="2";
 916 \end_layout
 917
 918 \begin_layout Plain Layout
 919
 920 (14,-7) *{}="3";
 921 \end_layout
 922
 923 \begin_layout Plain Layout
 924
 925 (14,-13)*{}="3'";
 926 \end_layout
 927
 928 \begin_layout Plain Layout
 929
 930 (18,0) *={}="";
 931 \end_layout
 932
 933 \begin_layout Plain Layout
 934
 935 "1";"2" **
 936 \backslash
 937 crv{(-4,-21)&(5,-15)};
 938 \end_layout
 939
 940 \begin_layout Plain Layout
 941
 942 ?(.15)*
 943 \backslash
 944 dir{<}+(5,10)*{
 945 \backslash
 946 overline{F(x)}};
 947 \end_layout
 948
 949 \begin_layout Plain Layout
 950
 951 "2";"3" **
 952 \backslash
 953 crv{(6,1)&(14,1)};
 954 \end_layout
 955
 956 \begin_layout Plain Layout
 957
 958 ?(0)*
 959 \backslash
 960 dir{<}+(4,8)*{
 961 \backslash
 962 widetilde{F(i_x)}} ;
 963 \end_layout
 964
 965 \begin_layout Plain Layout
 966
 967 ?(.95)*
 968 \backslash
 969 dir{<}+(5,-2)*{F(
 970 \backslash
 971 overline x)};
 972 \end_layout
 973
 974 \begin_layout Plain Layout
 975
 976 "3";"3'" **
 977 \backslash
 978 dir{-};
 979 \end_layout
 980
 981 \begin_layout Plain Layout
 982
 983 (-2,6)*{}="X1";
 984 \end_layout
 985
 986 \begin_layout Plain Layout
 987
 988 (-10,6)*{}="X2";
 989 \end_layout
 990
 991 \begin_layout Plain Layout
 992
 993 "X1";"X2" **
 994 \backslash
 995 crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
 996 \end_layout
 997
 998 \begin_layout Plain Layout
 999
1000 (-2,-6)*{}="XA";
1001 \end_layout
1002
1003 \begin_layout Plain Layout
1004
1005 (-10,-6)*{}="XB";
1006 \end_layout
1007
1008 \begin_layout Plain Layout
1009
1010 "XA";"XB" **
1011 \backslash
1012 crv{~*=<2pt>{.}(-2,1)&(-10,1)};
1013 \end_layout
1014
1015 \begin_layout Plain Layout
1016
1017
1018 \backslash
1019 endxy
1020 \end_layout
1021
1022 \end_inset
1023
1024
1025 \end_layout
1026
1027 \end_inset
1028
1029
1030 \end_layout
1031
1032 \begin_layout Description
1033 Categories
1034 \end_layout
1035
1036 \begin_layout Standard
1037 \begin_inset Preview
1038
1039 \begin_layout Standard
1040 \begin_inset ERT
1041 status collapsed
1042
1043 \begin_layout Plain Layout
1044
1045
1046 \backslash
1047 xymatrix{
1048 \end_layout
1049
1050 \begin_layout Plain Layout
1051
1052 (x
1053 \backslash
1054 otimes 1)
1055 \backslash
1056 otimes y
1057 \end_layout
1058
1059 \begin_layout Plain Layout
1060
1061
1062 \backslash
1063 ar[rr]^{a_{x,1,y}}
1064 \end_layout
1065
1066 \begin_layout Plain Layout
1067
1068
1069 \backslash
1070 ar[dr]_{r_x
1071 \backslash
1072 otimes 1_y}
1073 \end_layout
1074
1075 \begin_layout Plain Layout
1076
1077 && x
1078 \backslash
1079 otimes(1
1080 \backslash
1081 otimes y)
1082 \end_layout
1083
1084 \begin_layout Plain Layout
1085
1086
1087 \backslash
1088 ar[dl]^{1_x
1089 \backslash
1090 otimes
1091 \backslash
1092 ell_y }
1093 \backslash
1094
1095 \backslash
1096
1097 \end_layout
1098
1099 \begin_layout Plain Layout
1100
1101 & x
1102 \backslash
1103 otimes y }
1104 \end_layout
1105
1106 \end_inset
1107
1108
1109 \end_layout
1110
1111 \end_inset
1112
1113
1114 \begin_inset Preview
1115
1116 \begin_layout Standard
1117 \begin_inset ERT
1118 status collapsed
1119
1120 \begin_layout Plain Layout
1121
1122
1123 \backslash
1124 xy
1125 \end_layout
1126
1127 \begin_layout Plain Layout
1128
1129 (-9,0)*+{
1130 \backslash
1131 bullet}="1";
1132 \end_layout
1133
1134 \begin_layout Plain Layout
1135
1136 (0,0)*+{
1137 \backslash
1138 bullet}="2";
1139 \end_layout
1140
1141 \begin_layout Plain Layout
1142
1143 {
1144 \backslash
1145 ar@/^.9pc/ "1";"2"};
1146 \end_layout
1147
1148 \begin_layout Plain Layout
1149
1150 {
1151 \backslash
1152 ar@/_.9pc/ "1";"2"};
1153 \end_layout
1154
1155 \begin_layout Plain Layout
1156
1157 {
1158 \backslash
1159 ar@/^2pc/ "1";"2"};
1160 \end_layout
1161
1162 \begin_layout Plain Layout
1163
1164 {
1165 \backslash
1166 ar@/_2pc/ "1";"2"};
1167 \end_layout
1168
1169 \begin_layout Plain Layout
1170
1171 {
1172 \backslash
1173 ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
1174 \end_layout
1175
1176 \begin_layout Plain Layout
1177
1178 {
1179 \backslash
1180 ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
1181 \end_layout
1182
1183 \begin_layout Plain Layout
1184
1185 {
1186 \backslash
1187 ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
1188 \end_layout
1189
1190 \begin_layout Plain Layout
1191
1192 (0,0)*+{
1193 \backslash
1194 bullet}="1";
1195 \end_layout
1196
1197 \begin_layout Plain Layout
1198
1199 (9,0)*+{
1200 \backslash
1201 bullet}="2";
1202 \end_layout
1203
1204 \begin_layout Plain Layout
1205
1206 (18,0)*+{
1207 \backslash
1208 bullet}="3";
1209 \end_layout
1210
1211 \begin_layout Plain Layout
1212
1213 {
1214 \backslash
1215 ar "1";"2"};
1216 \end_layout
1217
1218 \begin_layout Plain Layout
1219
1220 {
1221 \backslash
1222 ar "2";"3"};
1223 \end_layout
1224
1225 \begin_layout Plain Layout
1226
1227 {
1228 \backslash
1229 ar@/^1pc/ "1";"2"};
1230 \end_layout
1231
1232 \begin_layout Plain Layout
1233
1234 {
1235 \backslash
1236 ar@/_1pc/ "1";"2"};
1237 \end_layout
1238
1239 \begin_layout Plain Layout
1240
1241 {
1242 \backslash
1243 ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
1244 \end_layout
1245
1246 \begin_layout Plain Layout
1247
1248 {
1249 \backslash
1250 ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
1251 \end_layout
1252
1253 \begin_layout Plain Layout
1254
1255
1256 \backslash
1257 endxy
1258 \end_layout
1259
1260 \end_inset
1261
1262
1263 \end_layout
1264
1265 \end_inset
1266
1267
1268 \end_layout
1269
1270 \begin_layout Description
1271 Transformations
1272 \end_layout
1273
1274 \begin_layout Standard
1275 \begin_inset Preview
1276
1277 \begin_layout Standard
1278 \begin_inset ERT
1279 status collapsed
1280
1281 \begin_layout Plain Layout
1282
1283
1284 \backslash
1285 xy %FIG.19.
1286  Natural transformation between functors.
1287 \end_layout
1288
1289 \begin_layout Plain Layout
1290
1291 (-26,-2)*+{
1292 \backslash
1293 bullet}="a";
1294 \end_layout
1295
1296 \begin_layout Plain Layout
1297
1298 (-12,3)*+{
1299 \backslash
1300 bullet}="b";
1301 \end_layout
1302
1303 \begin_layout Plain Layout
1304
1305 (-16,-5)*+{
1306 \backslash
1307 bullet}="c";
1308 \end_layout
1309
1310 \begin_layout Plain Layout
1311
1312 {
1313 \backslash
1314 ar@/^.25pc/ "a";"b"};
1315 \end_layout
1316
1317 \begin_layout Plain Layout
1318
1319 {
1320 \backslash
1321 ar@/_.25pc/"a";"c"};
1322 \end_layout
1323
1324 \begin_layout Plain Layout
1325
1326 {
1327 \backslash
1328 ar@/_.15pc/ "b";"c"};
1329 \end_layout
1330
1331 \begin_layout Plain Layout
1332
1333 %START TOP
1334 \end_layout
1335
1336 \begin_layout Plain Layout
1337
1338 (12,10)*+{
1339 \backslash
1340 bullet}="ta";
1341 \end_layout
1342
1343 \begin_layout Plain Layout
1344
1345 (26,15)*+{
1346 \backslash
1347 bullet}="tb";
1348 \end_layout
1349
1350 \begin_layout Plain Layout
1351
1352 (22,8)*+{
1353 \backslash
1354 bullet}="tc";
1355 \end_layout
1356
1357 \begin_layout Plain Layout
1358
1359 {
1360 \backslash
1361 ar@/^.25pc/ "ta";"tb"};
1362 \end_layout
1363
1364 \begin_layout Plain Layout
1365
1366 {
1367 \backslash
1368 ar@/_.25pc/ "ta";"tc"};
1369 \end_layout
1370
1371 \begin_layout Plain Layout
1372
1373 {
1374 \backslash
1375 ar@/_.15pc/ "tb";"tc"};
1376 \end_layout
1377
1378 \begin_layout Plain Layout
1379
1380 %START bottom
1381 \end_layout
1382
1383 \begin_layout Plain Layout
1384
1385 (12,-10)*+{
1386 \backslash
1387 bullet}="ba";
1388 \end_layout
1389
1390 \begin_layout Plain Layout
1391
1392 (26,-5)*+{
1393 \backslash
1394 bullet}="bb";
1395 \end_layout
1396
1397 \begin_layout Plain Layout
1398
1399 (22,-12)*+{
1400 \backslash
1401 bullet}="bc";
1402 \end_layout
1403
1404 \begin_layout Plain Layout
1405
1406 {
1407 \backslash
1408 ar@/^.25pc/@{.>} "ba";"bb"};
1409 \end_layout
1410
1411 \begin_layout Plain Layout
1412
1413 {
1414 \backslash
1415 ar@/_.25pc/ "ba";"bc"};
1416 \end_layout
1417
1418 \begin_layout Plain Layout
1419
1420 {
1421 \backslash
1422 ar@/_.15pc/ "bb";"bc"};
1423 \end_layout
1424
1425 \begin_layout Plain Layout
1426
1427 %START CONNECT
1428 \end_layout
1429
1430 \begin_layout Plain Layout
1431
1432 {
1433 \backslash
1434 ar@/_.15pc/ "ta";"ba"};
1435 \end_layout
1436
1437 \begin_layout Plain Layout
1438
1439 {
1440 \backslash
1441 ar@/_.15pc/ "tb";"bb"};
1442 \end_layout
1443
1444 \begin_layout Plain Layout
1445
1446 {
1447 \backslash
1448 ar@/_.15pc/ "tc";"bc"};
1449 \end_layout
1450
1451 \begin_layout Plain Layout
1452
1453 %START ARROWS AND LABELS
1454 \end_layout
1455
1456 \begin_layout Plain Layout
1457
1458 (-12,6)*{}="DF";
1459 \end_layout
1460
1461 \begin_layout Plain Layout
1462
1463 (6,10)*{}="CF";
1464 \end_layout
1465
1466 \begin_layout Plain Layout
1467
1468 {
1469 \backslash
1470 ar@/^.35pc/^F "DF";"CF"};
1471 \end_layout
1472
1473 \begin_layout Plain Layout
1474
1475 (-12,-6)*{}="DF";
1476 \end_layout
1477
1478 \begin_layout Plain Layout
1479
1480 (6,-10)*{}="CF";
1481 \end_layout
1482
1483 \begin_layout Plain Layout
1484
1485 {
1486 \backslash
1487 ar@/_.35pc/_G "DF";"CF"};
1488 \end_layout
1489
1490 \begin_layout Plain Layout
1491
1492 (-2,5)*{}="DF";
1493 \end_layout
1494
1495 \begin_layout Plain Layout
1496
1497 (-2,-5)*{}="CF";
1498 \end_layout
1499
1500 \begin_layout Plain Layout
1501
1502 {
1503 \backslash
1504 ar@{=>}^{
1505 \backslash
1506 alpha} "DF";"CF"};
1507 \end_layout
1508
1509 \begin_layout Plain Layout
1510
1511 (29,3)*{D};
1512 \end_layout
1513
1514 \begin_layout Plain Layout
1515
1516 (-23,3)*{C};
1517 \end_layout
1518
1519 \begin_layout Plain Layout
1520
1521
1522 \backslash
1523 endxy
1524 \end_layout
1525
1526 \end_inset
1527
1528
1529 \end_layout
1530
1531 \end_inset
1532
1533
1534 \end_layout
1535
1536 \begin_layout Section
1537 IPA
1538 \end_layout
1539
1540 \begin_layout Standard
1541 \begin_inset Preview
1542
1543 \begin_layout Standard
1544 \begin_inset ERT
1545 status collapsed
1546
1547 \begin_layout Plain Layout
1548
1549
1550 \backslash
1551 textipa{Ekspl@"neIS@n}
1552 \end_layout
1553
1554 \end_inset
1555
1556
1557 \end_layout
1558
1559 \end_inset
1560
1561
1562 \end_layout
1563
1564 \begin_layout Section
1565 QTree
1566 \end_layout
1567
1568 \begin_layout Standard
1569 \begin_inset Preview
1570
1571 \begin_layout Standard
1572 \begin_inset ERT
1573 status collapsed
1574
1575 \begin_layout Plain Layout
1576
1577
1578 \backslash
1579 Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ]
1580 \end_layout
1581
1582 \end_inset
1583
1584
1585 \end_layout
1586
1587 \end_inset
1588
1589
1590 \begin_inset Preview
1591
1592 \begin_layout Standard
1593 \begin_inset ERT
1594 status collapsed
1595
1596 \begin_layout Plain Layout
1597
1598
1599 \backslash
1600 Tree [.$
1601 \backslash
1602 sigma$ $
1603 \backslash
1604 mu$ $
1605 \backslash
1606 mu$ ]
1607 \end_layout
1608
1609 \end_inset
1610
1611
1612 \end_layout
1613
1614 \end_inset
1615
1616
1617 \end_layout
1618
1619 \end_body
1620 \end_document