Paths in double categories
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| Venue: | Theory Appl. Categ |
| Citations: | 4 - 1 self |
BibTeX
@ARTICLE{Dawson_pathsin,
author = {R. J. Macg Dawson and R. Paré and D. A. Pronk},
title = {Paths in double categories},
journal = {Theory Appl. Categ},
year = {},
volume = {16},
pages = {2006}
}
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Abstract
Abstract. Two constructions of paths in double categories are studied, providing algebraic versions of the homotopy groupoid of a space. Universal properties of these constructions are presented. The first is seen as the codomain of the universal oplax morphism of double categories and the second, which is a quotient of the first, gives the universal normal oplax morphism. Normality forces an equivalence relation on cells, a special case of which was seen before in the free adjoint construction. These constructions are the object part of 2-comonads which are shown to be oplax idempotent. The coalgebras for these comonads turn out to be Leinster’s fc-multicategories, with representable identities in the second case.
