nLab
fibrant object

Context

Model category theory

model category

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

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

Model structures

for \infty-groupoids

for ∞-groupoids

for nn-groupoids

for \infty-groups

for \infty-algebras

general

specific

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 object XX is said to be fibrant if the unique map X1X\to 1 to the terminal object is a fibration.

Dually, XX is said to be cofibrant if the unique map 0X0\to X from the initial object is a cofibration.

Revised on May 12, 2014 01:32:16 by Urs Schreiber (31.55.60.16)