nLab
trivial model structure

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

Definition

Every category CC with limits and colimits becomes a model category by setting

  • the weak equivalences are the isomorphisms;

  • every morphism is a fibration;

  • every morphism is a cofibration.

This model structure regards CC as an (∞,1)-category with only trivial k-morphisms for k2k \geq 2.

Revised on January 28, 2012 09:38:31 by Mike Shulman (71.136.231.206)