Geodesic
Higher monodromy
Homology, homotopy, and applications, Tome 7 (2005) no. 1, pp. 109-150.

Voir la notice de l'article provenant de la source International Press of Boston

For a given category $C$ and a topological space $X$, the constant stack on $X$ with stalk $C$ is the stack of locally constant sheaves with values in $C$. Its global objects are classified by their monodromy, a functor from the fundamental groupoid $Π_1(X)$ to $C$. In this paper we recall these notions from the point of view of higher category theory and then define the 2-monodromy of a locally constant stack with values in a 2-category $C$ as a 2-functor from the homotopy 2-groupoid $Π_2(X)$ to $C$. We show that 2-monodromy classifies locally constant stacks on a reasonably well-behaved space $X$. As an application, we show how to recover from this classification the cohomological version of a classical theorem of Hopf, and we extend it to the non abelian case.
DOI : 10.4310/HHA.2005.v7.n1.a7
Classification : 14A20, 18G50, 55Pxx
Keywords: monodromy representation, algebraic topology, stacks, category theory, non abelian cohomology 
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Pietro Polesello; Ingo Waschkies. Higher monodromy. Homology, homotopy, and applications, Tome 7 (2005) no. 1, pp. 109-150. doi : 10.4310/HHA.2005.v7.n1.a7. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2005.v7.n1.a7/

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