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‎foundations/glue/index.html‎

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</style></head><body class="content"></body></html><html><head><meta property="og:title" content="GLUE"><meta property="og:description" content="Glue Types"><meta property="og:url" content="https://urs.groupoid.space/foundations/glue/"></head></html><title>GLUE</title><nav><a href='../../index.html'>ANDERS</a>
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</style></head><body class="content"></body></html><html><head><meta property="og:title" content="GLUE"><meta property="og:description" content="Glue Types"><meta property="og:url" content="https://urs.groupoid.space/foundations/glue/"></head></html><title>GLUE</title><nav><a href='../../index.html'>URS</a>
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<a href='../../lib/index.html'>LIB</a>
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<a href='#'>GLUE</a></nav><article class="main list"><section><h1>GLUE</h1><aside><time>Published: 29 OCT 2023</time></aside><p><mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.023ex;" xmlns="http://www.w3.org/2000/svg" width="5.405ex" height="1.6ex" role="img" focusable="false" viewBox="0 -697 2389 707" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-401-TEX-B-1D406" d="M465 -10Q281 -10 173 88T64 343Q64 413 85 471T143 568T217 631T298 670Q371 697 449 697Q452 697 459 697T470 696Q502 696 531 690T582 675T618 658T644 641T656 632L732 695Q734 697 745 697Q758 697 761 692T765 668V627V489V449Q765 428 761 424T741 419H731H724Q705 419 702 422T695 444Q683 520 631 577T495 635Q364 635 295 563Q261 528 247 477T232 343Q232 296 236 260T256 185T296 120T366 76T472 52Q481 51 498 51Q544 51 573 67T607 108Q608 111 608 164V214H464V276H479Q506 273 680 273Q816 273 834 276H845V214H765V113V51Q765 16 763 8T750 0Q742 2 709 16T658 40L648 46Q592 -10 465 -10Z"></path><path id="MJX-401-TEX-B-1D425" d="M43 686L134 690Q225 694 226 694H232V62H301V0H292Q274 3 170 3Q67 3 49 0H40V62H109V332Q109 387 109 453T110 534Q110 593 108 605T94 620Q80 624 53 624H40V686H43Z"></path><path id="MJX-401-TEX-B-1D42E" d="M40 442L134 446Q228 450 229 450H235V273V165Q235 90 238 74T254 52Q268 46 304 46H319Q352 46 380 67T419 121L420 123Q424 135 425 199Q425 201 425 207Q425 233 425 249V316Q425 354 423 363T410 376Q396 380 369 380H356V442L554 450V267Q554 84 556 79Q561 62 610 62H623V31Q623 0 622 0Q603 0 527 -3T432 -6Q431 -6 431 25V56L420 45Q373 6 332 -1Q313 -6 281 -6Q208 -6 165 14T109 87L107 98L106 230Q106 358 104 366Q96 380 50 380H37V442H40Z"></path><path id="MJX-401-TEX-B-1D41E" d="M32 225Q32 332 102 392T272 452H283Q382 452 436 401Q494 343 494 243Q494 226 486 222T440 217Q431 217 394 217T327 218H175V209Q175 177 179 154T196 107T236 69T306 50Q312 49 323 49Q376 49 410 85Q421 99 427 111T434 127T442 133T463 135H468Q494 135 494 117Q494 110 489 97T468 66T431 32T373 5T292 -6Q181 -6 107 55T32 225ZM383 276Q377 346 348 374T280 402Q253 402 230 390T195 357Q179 331 176 279V266H383V276Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD"><g data-mml-node="mi"><use data-c="1D406" xlink:href="#MJX-401-TEX-B-1D406"></use><use data-c="1D425" xlink:href="#MJX-401-TEX-B-1D425" transform="translate(904,0)"></use><use data-c="1D42E" xlink:href="#MJX-401-TEX-B-1D42E" transform="translate(1223,0)"></use><use data-c="1D41E" xlink:href="#MJX-401-TEX-B-1D41E" transform="translate(1862,0)"></use></g></g></g></g></svg></mjx-container> types defines composition structure for fibrant
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universes that allows partial elements to be extended

‎foundations/glue/index.pug‎

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‎foundations/path/index.html‎

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</style></head><body class="content"></body></html><html><head><meta property="og:title" content="PATH"><meta property="og:description" content="Path Space"><meta property="og:url" content="https://urs.groupoid.space/foundations/path/"></head></html><title>PATH</title><nav><a href='../../index.html'>ANDERS</a>
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</style></head><body class="content"></body></html><html><head><meta property="og:title" content="PATH"><meta property="og:description" content="Path Space"><meta property="og:url" content="https://urs.groupoid.space/foundations/path/"></head></html><title>PATH</title><nav><a href='../../index.html'>URS</a>
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<a href='#'>PATH</a></nav><article class="main list"><div class="exe"><section><h1>PATH SPACES</h1><aside><time>Published: 25 JUL 2018</time></aside><p>The homotopy identity system defines a <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.014ex;" xmlns="http://www.w3.org/2000/svg" width="5.5ex" height="1.584ex" role="img" focusable="false" viewBox="0 -694 2431 700" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-592-TEX-B-1D40F" d="M400 0Q376 3 226 3Q75 3 51 0H39V62H147V624H39V686H253Q435 686 470 685T536 678Q585 668 621 648T675 605T705 557T718 514T721 483T718 451T704 409T673 362T616 322T530 293Q500 288 399 287H304V62H412V0H400ZM553 475Q553 554 537 582T459 622Q451 623 373 624H298V343H372Q457 344 480 350Q527 362 540 390T553 475Z"></path><path id="MJX-592-TEX-B-1D41A" d="M64 349Q64 399 107 426T255 453Q346 453 402 423T473 341Q478 327 478 310T479 196V77Q493 63 529 62Q549 62 553 57T558 31Q558 9 552 5T514 0H497H481Q375 0 367 56L356 46Q300 -6 210 -6Q130 -6 81 30T32 121Q32 188 111 226T332 272H350V292Q350 313 348 327T337 361T306 391T248 402T194 399H189Q204 376 204 354Q204 327 187 306T134 284Q97 284 81 305T64 349ZM164 121Q164 89 186 67T238 45Q274 45 307 63T346 108L350 117V226H347Q248 218 206 189T164 121Z"></path><path id="MJX-592-TEX-B-1D42D" d="M272 49Q320 49 320 136V145V177H382V143Q382 106 380 99Q374 62 349 36T285 -2L272 -5H247Q173 -5 134 27Q109 46 102 74T94 160Q94 171 94 199T95 245V382H21V433H25Q58 433 90 456Q121 479 140 523T162 621V635H224V444H363V382H224V239V207V149Q224 98 228 81T249 55Q261 49 272 49Z"></path><path id="MJX-592-TEX-B-1D421" d="M40 686L131 690Q222 694 223 694H229V533L230 372L238 381Q248 394 264 407T317 435T398 450Q428 450 448 447T491 434T529 402T551 346Q553 335 554 198V62H623V0H614Q596 3 489 3Q374 3 365 0H356V62H425V194V275Q425 348 416 373T371 399Q326 399 288 370T238 290Q236 281 235 171V62H304V0H295Q277 3 171 3Q64 3 46 0H37V62H106V332Q106 387 106 453T107 534Q107 593 105 605T91 620Q77 624 50 624H37V686H40Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD"><g data-mml-node="mi"><use data-c="1D40F" xlink:href="#MJX-592-TEX-B-1D40F"></use><use data-c="1D41A" xlink:href="#MJX-592-TEX-B-1D41A" transform="translate(786,0)"></use><use data-c="1D42D" xlink:href="#MJX-592-TEX-B-1D42D" transform="translate(1345,0)"></use><use data-c="1D421" xlink:href="#MJX-592-TEX-B-1D421" transform="translate(1792,0)"></use></g></g></g></g></svg></mjx-container>
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space indexed over type <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: 0;" xmlns="http://www.w3.org/2000/svg" width="1.697ex" height="1.62ex" role="img" focusable="false" viewBox="0 -716 750 716" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-593-TEX-I-1D434" d="M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D434" xlink:href="#MJX-593-TEX-I-1D434"></use></g></g></g></svg></mjx-container>

‎foundations/path/index.pug‎

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