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Q: Computing morphisms between stalks of proper pushforward sheaf

shadow10Consider the map $\pi : (0,n]\to S^1$ sending $t\mapsto e^{2\pi it}$ and let's look at the proper pushforward sheaf $F\cong \pi_!\mathbb{C}_{(0,n]}$. The stalk of this sheaf is $\mathbb{C}^n$ at every point on $S^1$. Consider the paths, $\gamma_1(t)=t\pi$ and $\gamma_2(t)=(2-t)\pi$ connecting $0$...

In mathematics, a quiver is a directed graph where loops and multiple arrows between two vertices are allowed, i.e. a multidigraph. They are commonly used in representation theory: a representation V of a quiver assigns a vector space V(x) to each vertex x of the quiver and a linear map V(a) to each arrow a. In category theory, a quiver can be understood to be the underlying structure of a category, but without composition or a designation of identity morphisms. That is, there is a forgetful functor from Cat to Quiv. Its left adjoint is a free functor which, from a quiver, makes the corresponding...
 

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