nLab trivial model structure


Model category theory

model category, model \infty -category



Universal constructions


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


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.

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