2-Groupoid Enrichments in Homotopy Theory and Algebra by Kamps K.H., Porter T. PDF

By Kamps K.H., Porter T.

Show description

Read or Download 2-Groupoid Enrichments in Homotopy Theory and Algebra PDF

Best algebra books

Linear algebra: An introduction - download pdf or read online

During this beautiful and well-written textual content, Richard Bronson offers readers a substructure for an organization realizing of the summary innovations of linear algebra and its purposes. the writer begins with the concrete and computational, and leads the reader to a call of significant purposes (Markov chains, least-squares approximation, and answer of differential equations utilizing Jordan basic form).

Extra info for 2-Groupoid Enrichments in Homotopy Theory and Algebra

Example text

Math. Belg. 41 (1989), 219–247. , Hardie, K. , Kamps, K. H. : A homotopy double groupoid of a Hausdorff space, Theory Appl. Categ. 10 (2002) 71–93. Brown, R. : Crossed complexes and non-Abelian extensions, In: Category Theory, Applications to Algebra, Logic and Topology, Proceedings, Gummersbach, 1981, Lecture Notes in Math. 962, Springer, Berlin, 1982, pp. 39–50. Brown, R. and Mosa, G. : Double categories, 2-categories, thin structures and connections, Theory Appl. Categ. 5 (1999), 163–175. : Modules crois´es g´en´eralis´es de longueur 2, J.

A 3-type is representable by a (G2 , ⊗)-groupoid as we have noted and the category of 2types ‘is’ the ‘category’ of 2-groupoids. An action of a 3-type on a 2-type can thus be studied via (G2 , ⊗)-functors (or lax-versions of them) from a 3-type model to the (G2 , ⊗)-category of 2-groupoids itself. (Grothendieck viewed his programme as part of a higher dimensionl Galois theory. ) 4. Conclusion We have tried to indicate some of the ways in which (G2 , ⊗)-categories arise in algebra and topology, both as large examples such as Top and Ch and small ones modelling homotopy 3-types or as braided monoidal categories that might arise as categories of representations.

Abstract homotopy theory: the interaction of category theory and homotopy theory, Preprint, 2001. : Homotopy types of strict 3-groupoids, e-print math. CT/9810059, Toulouse, 1998. html. : Categorical structures, In: Handbook of Algebra, Vol. 1, Elsevier, Amsterdam, 1996, pp. 529–577. : The role of Batanin’s monoidal globular categories, In: E. Getzler et al. (eds), Higher Category Theory. Workshop on Higher Category Theory and Physics (Evanston, 1997), Contemp. Math. 230, Amer. Math. , Providence, 1998, pp.

Download PDF sample

2-Groupoid Enrichments in Homotopy Theory and Algebra by Kamps K.H., Porter T.

by David

Rated 4.86 of 5 – based on 48 votes