#
Quotient models of a category up to directed homotopy

##
Marco Grandis

Directed Algebraic Topology is a recent field, deeply linked with ordinary and
higher dimensional Category Theory. A `directed space', e.g. an ordered
topological space, has directed homotopies (which are generally non reversible)
and a fundamental *category* (replacing the fundamental groupoid of the
classical case). Finding a simple - possibly finite - model of the latter is a
non-trivial problem, whose solution gives relevant information on the given
`space'; a problem which is of interest for applications as well as in general
Category Theory.
Here we continue the work ``The shape of a category up to directed homotopy",
with a deeper analysis of `surjective models', motivated by studying the
singularities of 3-dimensional ordered spaces.

Keywords:
homotopy theory, adjunctions, reflective subcategories, directed algebraic
topology, fundamental
category, concurrent processes

2000 MSC:
55Pxx, 18A40, 68Q85

*Theory and Applications of Categories,*
Vol. 16, 2006,
No. 26, pp 709-735.

http://www.tac.mta.ca/tac/volumes/16/26/16-26.dvi

http://www.tac.mta.ca/tac/volumes/16/26/16-26.ps

http://www.tac.mta.ca/tac/volumes/16/26/16-26.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/16/26/16-26.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/16/26/16-26.ps

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