{"id":"openai-math/The-Grothendieck-homotopy-hypothesis-via-elementary-expansions","pdf":"https://github.com/openai/math/blob/main/preprints/The-Grothendieck-homotopy-hypothesis-via-elementary-expansions-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-Grothendieck-homotopy-hypothesis-via-elementary-expansions-September-24-2026","tags":["higher-category-theory","homotopy-theory","infinity-groupoids","grothendieck-hypothesis"],"score":0,"title":"The Grothendieck homotopy hypothesis via elementary expansions","domain":"Topology","family":"312","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.GT","summary":"We prove the Grothendieck homotopy hypothesis for every Grothendieck coherator in the Ara–Henry convention: its weak globular infinity-groupoids recover the homotopy theory of spaces. We also resolve Henry's pushout conjecture, showing that elementary expansions preserve components and all homotopy groups of cellular infinity-groupoids.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":true,"family_title":"The Grothendieck homotopy hypothesis"}