Geodesic
Transformation double categories associated to 2-group actions
Theory and applications of categories, Tome 30 (2015), pp. 1429-1468 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

Voir la notice de l'article

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.

Publié le :
Classification : 18B40, 18D10, 20L99
Keywords: 2-group, categorical group, crossed module, action, double category, adjoint action 
@article{TAC_2015_30_a42,
     author = {Jeffrey C. Morton and Roger Picken},
     title = {Transformation double categories associated to 2-group actions},
     journal = {Theory and applications of categories},
     pages = {1429--1468},
     year = {2015},
     volume = {30},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2015_30_a42/}
}
TY  - JOUR
AU  - Jeffrey C. Morton
AU  - Roger Picken
TI  - Transformation double categories associated to 2-group actions
JO  - Theory and applications of categories
PY  - 2015
SP  - 1429
EP  - 1468
VL  - 30
UR  - http://geodesic.mathdoc.fr/item/TAC_2015_30_a42/
LA  - en
ID  - TAC_2015_30_a42
ER  - 
%0 Journal Article
%A Jeffrey C. Morton
%A Roger Picken
%T Transformation double categories associated to 2-group actions
%J Theory and applications of categories
%D 2015
%P 1429-1468
%V 30
%U http://geodesic.mathdoc.fr/item/TAC_2015_30_a42/
%G en
%F TAC_2015_30_a42
Jeffrey C. Morton; Roger Picken. Transformation double categories associated to 2-group actions. Theory and applications of categories, Tome 30 (2015), pp. 1429-1468. http://geodesic.mathdoc.fr/item/TAC_2015_30_a42/