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Combinatorics of past-similarity in higher dimensional transition systems

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Philippe Gaucher

The key notion to understand the left determined Olschok model category
of star-shaped Cattani-Sassone transition systems is past-similarity.
Two states are past-similar if they have homotopic pasts. An object is
fibrant if and only if the set of transitions is closed under
past-similarity. A map is a weak equivalence if and only if it induces an
isomorphism after the identification of all past-similar states. The last
part of this paper is a discussion about the link between causality and
homotopy.

Keywords:
left determined model category,
combinatorial model category, discrete model structure, higher dimensional
transition system, causal structure, bisimulation

2010 MSC:
18C35,55U35,18G55,68Q85

*Theory and Applications of Categories,*
Vol. 32, 2017,
No. 33, pp 1107-1164.

Published 2017-08-29.

http://www.tac.mta.ca/tac/volumes/32/33/32-33.pdf

Revised 2017-09-08. Original version at:

http://www.tac.mta.ca/tac/volumes/32/33/32-33a.pdf

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