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nLab acyclic fibration

Context

Model category theory

model category, model \infty -category

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

Presentation of (,1)(\infty,1)-categories

Model structures

for \infty-groupoids

for ∞-groupoids

for equivariant \infty-groupoids

for rational \infty-groupoids

for rational equivariant \infty-groupoids

for nn-groupoids

for \infty-groups

for \infty-algebras

general \infty-algebras

specific \infty-algebras

for stable/spectrum objects

for (,1)(\infty,1)-categories

for stable (,1)(\infty,1)-categories

for (,1)(\infty,1)-operads

for (n,r)(n,r)-categories

for (,1)(\infty,1)-sheaves / \infty-stacks

Contents

Definition

In a model category, an acyclic fibration or trivial fibration is a morphism which is both a fibration and a weak equivalence.

Dually, an acyclic cofibration or trivial cofibration is a morphism which is both a cofibration and a weak equivalence.

Examples

Last revised on July 7, 2023 at 17:52:35. See the history of this page for a list of all contributions to it.