Università degli Studi di Genova


Cubical cospans and higher cobordisms (cospans in algebraic topology. III)

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.

Spans, cospans, weak double category, weak cubical category, cubical sets, homotopy pushout, cobordisms

18, 55

Pubblicato su: Journal of Homotopy and Related Structures Vol. 3 (2008) N. 1 Pag. 273-308