on chain complexes/model structure on cosimplicial abelian groups
related by the Dold-Kan correspondence
on algebras over an operad, on modules over an algebra over an operad
on dendroidal sets, for dendroidal complete Segal spaces, for dendroidal Cartesian fibrations
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 model category presentation of the (∞,1)-category ∞Grpd of all ∞-groupoid. Examples include:
on chain complexes/model structure on cosimplicial abelian groups
related by the Dold-Kan correspondence
model structure on cosimplicial simplicial sets and many more.