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.
Revised 2017-09-08. Original version at: