nLab Grpd

Redirected from "Groupoids".
Contents

Context

Category theory

Homotopy theory

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

categories of categories

Contents

Definition

The (2,1)-category GrpdGrpd is the 2-category whose

This is the full sub-2-category of Cat on those categories that are groupoids.

Properties

Presentation

One may regard GrpdGrpd 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)(2,1)-category.

References

On the local cartesian closure of the 2-category of groupoids (and the failure of this property for the 1-category version):

Discussion of GrpdGrpd as (with some tweaks) categorical semantics for homotopy type theory (the “groupoid model”, precursor to the simplicial set model):

category: category

Last revised on November 6, 2023 at 11:53:51. See the history of this page for a list of all contributions to it.