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
The basic example is formula_6 where on the right is the singular chain complex of "U" with coefficients in an abelian group "A".
Example: If "f" is a continuous map, then formula_7 is a cosheaf.