# nLab trivial model structure

### Context

#### Model category theory

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

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

Model structures

for $\infty$-groupoids

for ∞-groupoids

for equivariant $\infty$-groupoids

for rational $\infty$-groupoids

for rational equivariant $\infty$-groupoids

for $n$-groupoids

for $\infty$-groups

for $\infty$-algebras

general $\infty$-algebras

specific $\infty$-algebras

for stable/spectrum objects

for $(\infty,1)$-categories

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

for $(\infty,1)$-operads

for $(n,r)$-categories

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

## Definition

Every category $C$ 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 $C$ as an (∞,1)-category with only trivial k-morphisms for $k \geq 2$.

Last revised on January 28, 2012 at 09:38:31. See the history of this page for a list of all contributions to it.