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
The (2,1)-category $Grpd$ is the 2-category whose
2-morphisms are natural transformations, which are necessarily natural isomorphisms.
This is the full sub-2-category of Cat on those categories that are groupoids.
One may regard $Grpd$ also just as a 1-category by ignoring the natural isomorphisms between functors. This 1-category may be equipped with the natural model structure on groupoids to provide a 1-categorical presentation of the full $(2,1)$-category.