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Bicategorical homotopy pullbacks

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A.M. Cegarra, B.A. Heredia, J.Remedios

The homotopy theory of higher categorical structures has become a relevant
part of the machinery of algebraic topology and algebraic K-theory, and
this paper contains contributions to the study of the relationship between
Benabou's bicategories and the homotopy types of their classifying
spaces. Mainly, we state and prove an extension of Quillen's Theorem B by
showing, under reasonable necessary conditions, a bicategory-theoretical
interpretation of the homotopy-fibre product of the continuous maps
induced on classifying spaces by a diagram of bicategories
$A\to B \leftarrow A'$. Applications are given for the study of homotopy
pullbacks of monoidal categories and of crossed modules.

2010 MSC:
18D05, 18D10, 55P15, 55R65

*Theory and Applications of Categories,*
Vol. 30, 2015,
No. 6, pp 147-205.

Published 2015-02-09.

http://www.tac.mta.ca/tac/volumes/30/6/30-06.pdf

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