Pseudo Algebras and Pseudo Double Categories
Abstract
As an example of the categorical apparatus of pseudo algebras over 2-theories, we show that pseudo algebras over the 2-theory of categories can be viewed as pseudo double categories with folding or as appropriate 2-functors into bicategories. Foldings are equivalent to connection pairs, and also to thin structures if the vertical and horizontal morphisms coincide. In a sense, the squares of a double category with folding are determined in a functorial way by the 2-cells of the horizontal 2-category. As a special case, strict 2-algebras with one object and everything invertible are crossed modules under a group.
Cite
@article{arxiv.math/0608760,
title = {Pseudo Algebras and Pseudo Double Categories},
author = {Thomas M. Fiore},
journal= {arXiv preprint arXiv:math/0608760},
year = {2011}
}
Comments
60 pages. Exposition improved, Section 5 rewritten to include the 2-equivalence between crossed modules under groups and double groups with folding. This final version will appear in the Journal of Homotopy and Related Structures.