In topology, a branch of mathematics, a cosheaf with values in an
∞-categoryC 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.
Curry, Justin (2014). "§ 3, in particular Thm 3.10". Sheaves, cosheaves and applications (Doctoral dissertation). University of Pennsylvania. p. 34.
arXiv:1303.3255.
ProQuest1553207954.