can the statement “a simplicial set is the nerve of a category if and only if it satisfies a horn-filling condition” be tweaked for groupoids?
For some reason I convinced myself that a simplicial set (or maybe I mean directly Kan complex) is homotopy equivalent to the nerve of a groupoid if and only if it has no higher homotopy groups. Is ...
Given a topological space $X$, we may wish to consider it as an $(\infty,0)$-category, where the objects are the points of the space, the 1-morphisms are continuous paths between points, the ...
What are the ramifications of the fact that the first homotopy group can be non-commutative, whilst the higher homotopy groups can't be?
Does this mean that the first homotopy group in some sense contains more information than the higher homotopy groups? Is there another generalization of the fundamental group that can give rise to ...