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Algebraic colimit calculations in homotopy theory using fibred and cofibred categories

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Ronald Brown and Rafael Sivera

Higher Homotopy van Kampen Theorems allow some colimit calculations
of certain homotopical invariants of glued spaces. One corollary is
to describe homotopical excision in critical dimensions in terms of
induced modules and crossed modules over groupoids. This paper shows
how fibred and cofibred categories give an overall context for
discussing and computing such constructions, allowing one result to
cover many cases. A useful general result is that the inclusion of
a fibre of a fibred category preserves connected colimits. The main
homotopical applications are to pairs of spaces with several base
points; we also describe briefly applications to triads.

Keywords:
higher homotopy van Kampen theorems, homotopical excision,
colimits, fibred and cofibred categories, groupoids, modules,
crossed modules

2000 MSC:
55Q99, 18D30, 18A40

*Theory and Applications of Categories,*
Vol. 22, 2009,
No. 8, pp 222-251.

http://www.tac.mta.ca/tac/volumes/22/8/22-08.dvi

http://www.tac.mta.ca/tac/volumes/22/8/22-08.ps

http://www.tac.mta.ca/tac/volumes/22/8/22-08.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/22/8/22-08.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/22/8/22-08.ps

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