Università degli Studi di Genova
Every differentiable manifold X has a 'good cover', where all open sets and their finite intersections are contractible. Using a generalised van Kampen theorem for open covers we deduce that the fundamental groupoid of X is a 'generalised pushout' of codiscrete groupoids and inclusions. This fact motivates a brief study of generalised pushouts. In particular, we show that every groupoid is, up to equivalence, a generalised pushout of codiscrete subgroupoids, and that (in any category) finite generalised pushouts amount to ordinary pushouts and coequalisers.
fundamental groupoid, generalised pushout, colimit, differentiable manifold
Pubblicato su: Cahiers de Topologie et Geometrie Differentielle Categoriques Vol. 56 (2015) Pag. 232-240