#
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**

**Introductions**

**Definitions**

**Paths and cylinders**

**Homotopy groups**

**Basic facts**

**Theorems**

# Contents

## 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.
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