TY - JOUR
ID - 101064
TI - Six model categories for directed homotopy
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Gaucher, Philippe
AD - Universit\'e de Paris, CNRS, IRIF, F-75006, Paris, France.
Y1 - 2021
PY - 2021
VL - 15
IS - 1
SP - 145
EP - 181
KW - d-space
KW - flow
KW - topological model of concurrency
KW - combinatorial model category
KW - accessible model category
KW - locally presentable category
KW - enriched semicategory
KW - enriched non-unital category
DO - 10.52547/cgasa.15.1.145
N2 - We construct a q-model structure, an h-model structure and an m-model structure on multipointed $d$-spaces and on flows. The two q-model structures are combinatorial and left determined and they coincide with the combinatorial model structures already known on these categories. The four other model structures (the two m-model structures and the two h-model structures) are accessible. We give an example of multipointed $d$-space and of flow which are not cofibrant in any of the model structures. We explain why the m-model structures, Quillen equivalent to the q-model structure of the same category, are better behaved than the q-model structures.
UR - https://cgasa.sbu.ac.ir/article_101064.html
L1 - https://cgasa.sbu.ac.ir/article_101064_54e15c5a207051449a58ecc86c267e56.pdf
ER -