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Directed homotopy theory, II. Homotopy constructs

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Marco Grandis

Directed Algebraic Topology studies phenomena where privileged
directions appear, derived from the analysis of concurrency,
traffic networks, space-time models, etc.

This is the sequel of a paper, `Directed homotopy theory, I. The
fundamental category', where we introduced * directed spaces*,
their non reversible homotopies and their fundamental category.
Here we study some basic constructs of homotopy, like homotopy
pushouts and pullbacks, mapping cones and homotopy fibres,
suspensions and loops, cofibre and fibre sequences.

Keywords: homotopy theory, homotopical algebra, directed homotopy, homotopy
pushouts, homotopy pullbacks, mapping cones, homotopy fibres.

2000 MSC: 55P99, 18G55.

*Theory and Applications of Categories*, Vol. 10, 2002, No. 14, pp 369-391.

http://www.tac.mta.ca/tac/volumes/10/14/10-14.dvi

http://www.tac.mta.ca/tac/volumes/10/14/10-14.ps

http://www.tac.mta.ca/tac/volumes/10/14/10-14.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/10/14/10-14.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/10/14/10-14.ps

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