{
  "id": "grothendieck-infinity-groupoids-and-the-homotopy-hypothesis",
  "title": "Grothendieck infinity-groupoids and the homotopy hypothesis",
  "description": "Henry's pushout conjecture for every Grothendieck coherator, after OpenAI's 2026 proof: freely adjoining to a cellular infinity-groupoid a cell parallel to a given one, and a cell joining the two, is a weak equivalence. Globular theories and their models; the homotopy calculus; coskeletal cutoffs, spines and free shapes; trees and whiskers; partial cylinders and the main theorem; the canonical semi-model structure and the Quillen equivalence with spaces.",
  "units": [
    {
      "id": "globular-theories-and-their-models",
      "title": "Globular theories and their models",
      "reader": "globular-theories-and-their-models.html",
      "source": "src/globular-theories-and-their-models.md",
      "source_sha256": "67cd9760d15ea329e3141ab6bbd4f79cfd49c948d134af479dcaffefb97c491f",
      "status": "author_self_checked"
    },
    {
      "id": "the-homotopy-calculus",
      "title": "The homotopy calculus",
      "reader": "the-homotopy-calculus.html",
      "source": "src/the-homotopy-calculus.md",
      "source_sha256": "a71423f170b6379b14c726c681610831c55da61612b64e5f21530ec6cf6e8f46",
      "status": "author_self_checked"
    },
    {
      "id": "cutoffs-spines-and-free-shapes",
      "title": "Cutoffs, spines and free shapes",
      "reader": "cutoffs-spines-and-free-shapes.html",
      "source": "src/cutoffs-spines-and-free-shapes.md",
      "source_sha256": "6e47341a7c8fcd18fdfffe84ed1225a11c24738547dd86b6670b8aee3ef2481b",
      "status": "author_self_checked"
    },
    {
      "id": "trees-and-whiskers",
      "title": "Trees and whiskers",
      "reader": "trees-and-whiskers.html",
      "source": "src/trees-and-whiskers.md",
      "source_sha256": "1e317478283f52604241e9c11cd583b6f1e5e9b06ad3c945f119434382f486c5",
      "status": "author_self_checked"
    },
    {
      "id": "partial-cylinders-and-the-main-theorem",
      "title": "Partial cylinders and the main theorem",
      "reader": "partial-cylinders-and-the-main-theorem.html",
      "source": "src/partial-cylinders-and-the-main-theorem.md",
      "source_sha256": "26f525a743e863d3508b0e4dba649d3bfd4f167307208bd6785aa23e307e19e5",
      "status": "author_self_checked"
    },
    {
      "id": "the-semi-model-structure-and-the-homotopy-hypothesis",
      "title": "The semi-model structure and the homotopy hypothesis",
      "reader": "the-semi-model-structure-and-the-homotopy-hypothesis.html",
      "source": "src/the-semi-model-structure-and-the-homotopy-hypothesis.md",
      "source_sha256": "8b05050fa35ce0f5ea81da71a38eb5eae3057758c206a35b6eee0b8aa11bd83b",
      "status": "author_self_checked"
    }
  ],
  "prerequisites": [
    "basic category theory: presheaves, the Yoneda lemma (course Schemes, The functor of points and representability, Theorem 1.1) and left Kan extensions (course Derivators, Kan extensions and the derivator axioms, Theorem 2.1)",
    "test categories and Grothendieck's homotopy programme (course AG-AS), for context"
  ],
  "status": "author_self_checked",
  "proof_providers": "providers.json",
  "provenance": "provenance.json",
  "licence": "CC0-1.0"
}