The fundamental groupoid of a simplicial set $X$ is the localization $C[C^{-1}]$ of its category of simplices $C$ (a special case of the category of elements of a presheaf).
The fundamental groupoid of a simplicial set $X$ is the localization $C[C^{-1}]$ of its fundamental category $C$, defined as the left adjoint functor to the nerve functor
The fundamental groupoid of a simplicial set $X$ is a groupoid defined via the following system of generators and relations for a groupoid:
objects are precisely the vertices of $X$;
generating isomorphisms are precisely the edges of $X$;
for every 2-simplex of $X$ we have a relation
Created on October 25, 2019 at 17:47:17. See the history of this page for a list of all contributions to it.