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The classifying space of a categorical crossed module

✍ Scribed by Pilar Carrasco; Antonio M. Cegarra; Antonio R. Garzón

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
365 KB
Volume
283
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Any pointed CW‐complex X has associated a categorical crossed module WX whose homotopy groups coincide with those of the space up to dimension 3. Here we associate WX more closely with the homotopy 3‐type of X. We introduce the nerve of a categorical crossed module L and define its classifying space BL as the geometrical realization of the nerve. Then we prove that there is a map X → BWX inducing isomorphism of the homotopy groups π~i~ for i ≤ 3. Finally, comparison with other algebraic models of 3‐types is achieved (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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