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Università degli Studi di Genova |
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Università degli Studi di Genova |
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Abstract: After two papers on weak cubical categories and collarable cospans, respectively, we put things together and construct a weak cubical category of cubical collared cospans of topological spaces. We also build a second structure, called a quasi cubical category, formed of arbitrary cubical cospans concatenated by homotopy pushouts. This structure, simpler but weaker, has lax identities. It contains a similar framework for cobordisms of manifolds with corners and could therefore be the basis to extend the study of TQFT's of Part II to higher cubical degree. Keywords: Spans, cospans, weak double category, weak cubical category, cubical sets, homotopy pushout, cobordisms MSC: 18, 55 Pubblicato su: Journal of Homotopy and Related Structures Vol. 3 (2008) N. 1 Pag. 273-308 |