Geodesic
Paths in double categories
Theory and applications of categories, Tome 16 (2006), pp. 460-521 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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.

Classification : 18A40, 18C20, 18D05
Keywords: double categories, oplax double categories, paths, localisation 
@article{TAC_2006_16_a17,
     author = {R. J. MacG. Dawson and R. Par\'e and D. A. Pronk},
     title = {Paths in  double categories},
     journal = {Theory and applications of categories},
     pages = {460--521},
     year = {2006},
     volume = {16},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2006_16_a17/}
}
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R. J. MacG. Dawson; R. Paré; D. A. Pronk. Paths in  double categories. Theory and applications of categories, Tome 16 (2006), pp. 460-521. http://geodesic.mathdoc.fr/item/TAC_2006_16_a17/