Mathematics – Algebraic Topology
Scientific paper
2001-03-02
Theory and Applications of Categories, Vol. 11, 2003, No. 3, pp 75-106
Mathematics
Algebraic Topology
Final version ; see http://www.tac.mta.ca/tac/
Scientific paper
One can associate to any strict globular $\omega$-category three augmented simplicial nerves called the globular nerve, the branching and the merging semi-cubical nerves. If this strict globular $\omega$-category is freely generated by a precubical set, then the corresponding homology theories contain different informations about the geometry of the higher dimensional automaton modeled by the precubical set. Adding inverses in this $\omega$-category to any morphism of dimension greater than 2 and with respect to any composition laws of dimension greater than 1 does not change these homology theories. In such a framework, the globular nerve always satisfies the Kan condition. On the other hand, both branching and merging nerves never satisfy it, except in some very particular and uninteresting situations. In this paper, we introduce two new nerves (the branching and merging semi-globular nerves) satisfying the Kan condition and having conjecturally the same simplicial homology as the branching and merging semi-cubical nerves respectively in such framework. The latter conjecture is related to the thin elements conjecture already introduced in our previous papers.
No associations
LandOfFree
The branching nerve of HDA and the Kan condition does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The branching nerve of HDA and the Kan condition, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The branching nerve of HDA and the Kan condition will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-301448