categories: preprint : The branching nerve of HDA and the Kan condition

[Philippe Gaucher <gaucher@irmast2.u-strasbg.fr>]

Title : The branching nerve of HDA and the Kan condition

Abstract : We have already seen that in reasonable situations,
i.e. when the path $\omega$-category associated to a higher
dimensional automata (HDA) is an $\omega$-groupoid, only the globular
nerve satisfies the Kan condition. Indeed for the branching and
merging nerves, this condition generally does not hold. This drawback
is overcome here by introducing two new nerves (the left and right
globular nerves) satisfying the Kan condition in any reasonable
situation and having conjecturally the same simplicial homology as the
branching and merging nerves respectively for any $\omega$-category
freely generated by a cubical set.

Type : preprint

Comment : 22 pages ; any comments are welcome.

URLs : 

http://www-irma.u-strasbg.fr/~gaucher/fibrantcoin.ps.gz
http://www-irma.u-strasbg.fr/~gaucher/fibrantcoin.pdf