nLab
acyclic Kan fibration

Context

Homotopy theory

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

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Definition

A Kan fibration that at the same time is a weak homotopy equivalence is called an acyclic Kan fibration. (Also a trivial Kan fibration.)

Properties

Acyclic Kan fibrations are precisely the morphisms of simplicial sets that have the right lifting property against all simplex boundary inclusions.

They are the acyclic fibrations in the standard model structure on simplicial sets.

Last revised on November 9, 2015 at 07:27:19. See the history of this page for a list of all contributions to it.