#
Transformation double categories associated to 2-group actions

##
Jeffrey C. Morton and Roger Picken

Transformation groupoids associated to group actions capture the interplay
between global and local symmetries of structures described in
set-theoretic terms. This paper examines the analogous situation for
structures described in category-theoretic terms, where symmetry is
expressed as the action of a 2-group G (equivalently, a categorical
group) on a category C. It describes the construction of a
transformation groupoid in diagrammatic terms, and considers this
construction internal to Cat, the category of categories. The
result is a double category C//G which describes the local
symmetries of C. We define this and describe some of its structure,
with the adjoint action of G on itself as a guiding example.

Keywords:
2-group, categorical group, crossed module, action, double category,
adjoint action

2010 MSC:
18B40, 18D10, 20L99

*Theory and Applications of Categories,*
Vol. 30, 2015,
No. 43, pp 1429-1468.

Published 2015-10-26.

http://www.tac.mta.ca/tac/volumes/30/43/30-43.pdf

TAC Home