model category, model $\infty$-category
Definitions
Morphisms
Universal constructions
Refinements
Producing new model structures
Presentation of $(\infty,1)$-categories
Model structures
for $\infty$-groupoids
on chain complexes/model structure on cosimplicial abelian groups
related by the Dold-Kan correspondence
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
homotopy theory, (∞,1)-category theory, homotopy type theory
flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed…
models: topological, simplicial, localic, …
see also algebraic topology
Introductions
Definitions
Paths and cylinders
Homotopy groups
Basic facts
Theorems
A Reedy category with fibrant constants is a Reedy category $R$ such that for every model category $M$ and every fibrant object $X \in M$ the constant $R$-diagram at $X$ is Reedy fibrant.
For a Reedy category $R$ the following are equivalent.
This theorem is proven in Hirschhorn,Proposition 15.10.2 and Theorem 15.10.8.
The simplex category $\Delta$ is a Reedy category with fibrant constants.
More generally, Joyal’s disk categories $\Theta_n$ are Reedy categories with fibrant constants.
Every direct category is a Reedy category with fibrant constants.
Philip Hirschhorn, Model categories and their localizations, volume 99 of Mathematical Surveys and Monographs, American Mathematical Society, 2009,
Emily Riehl, Dominic Verity The theory and practice of Reedy categories arXiv
Last revised on October 7, 2013 at 09:05:26. See the history of this page for a list of all contributions to it.