n-types and n-fold structures

["Paoli, Simona (Dr.)" <sp424@leicester.ac.uk>]

Dear All,

   With regard to the recent postings about modelling general n-types and n-fold groupoids, I would like to point out the following. A proof of the modelling of general n-types (not only path-connected ones) using n-fold structures is given in the following research monograph, which I recently posted  on arVix:

S.Paoli, Segal-type models of higher categories, arXiv.1707.01868

The structure used there, called groupoidal weakly globular n-fold categories, is a subcategory of n-fold categories in which certain sub-structures are groupoidal, and satisfying several other conditions. This result is a proof of the homotopy hypothesis for a new model of weak n-categories, called  weakly globular n-fold categories, which is proved to be suitably equivalent to the Tamsamani-Simpson model.

In the above work there is also a proof that it is possible to use as fundamental functor from spaces to groupoidal weakly globular n-fold categories the construction found in the following paper

D. Blanc, S. Paoli, Segal-type algebraic models of n-types, Algebraic and Geometric Topology, 14  3419–3491.

This construction produces a functor from spaces to a subcategory of n-fold  groupoids.

Best wishes,

Simona.


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]