Cosheaf

In topology, a branch of mathematics, a cosheaf with values in an ∞-category C that admits colimits is a functor F from the category of open subsets of a topological space X (more precisely its nerve) to C such that

  • (1) The F of the empty set is the initial object.
  • (2) For any increasing sequence of open subsets with union U, the canonical map is an equivalence.
  • (3) is the pushout of and .

The basic example is where on the right is the singular chain complex of U with coefficients in an abelian group A.

Example:[1] If f is a continuous map, then is a cosheaf.

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