most recent 30 from http://mathoverflow.net 2013-05-20T21:28:19Z http://mathoverflow.net/feeds/question/16347 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/16347/homotopy-groups-of-cubical-sets David Roberts 2010-02-25T02:10:53Z 2010-02-25T02:10:53Z

<p>A cubical set $Box^{op} \to Set$ is a model for a homotopy type, via Grothendieck and Cisinski (here $Box$ is the box category with objects the natural numbers and arrows generated by face and degeneracy maps 'as usual'). A typical example is the singular cubical set of a space, $n \mapsto Hom(I^n,X)$. The homotopy groups of $X$ can be recovered from this cubical set as it satisfies a property analogous to that of Kan complexes (horns have fillers). In general, do the homotopy groups of a cubical set satisfying this 'Kan' condition agree with that of the homotopy type it represents?</p>