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Kan complex
- A simplicial set in which every horn (not just inner) admits a filler.
- Fibrant objects in simplicial sets.
Kan complex
- infinity categories
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homotopy type
If the the homotopy hypothesis holds, TFAE: - The infinity category of spaces (modeled by simplicial sets): take \({\mathsf{sSet}}\), take the Dweyer-Kan localization along weak homotopy equivalences, then take the homotopy coherent nerve. - Take the subcategory of Kan complexes that is enriched over \({\mathsf{Kan}}\) and use a standard mapping complex construction. - infinity groupoids, - anima