nLab
Grp

Contents

Definition

GrpGrp is the category with groups as objects and group homomorphisms as morphisms.

More abstractly, we can think of GrpGrp as the full subcategory of CatCat with groups as objects.

Remarks

Since groups may be identified with one-object groupoids, it is sometimes useful to regard GrpGrp as a 22-category, namely as the full sub-22-category of Grpd on one-object groupoids. In this case the 22-morphisms between homomorphisms of groups come from “intertwiners”: inner automorphisms of the target group.

On the other hand, if we regard GrpGrp as a full sub-22-category of Grpd *Grpd_*, the 22-category of pointed groups, then this is locally discrete and equivalent to the ordinary 11-category GrpGrp. This is because the only pointed intertwiner between two homomorphisms is the identity.

Precisely analogous statements hold for the category Alg of algebras.

category: category

Revised on June 13, 2013 17:27:08 by Urs Schreiber (82.169.65.155)