Idempotents in triangulated monoidal categories
Hogancamp, Matthew
Original · EN
In these notes we develop some basic theory of idempotents in monoidal categories. We introduce and study the notion of a pair of complementary idempotents in a triangulated monoidal category, as well as more general idempotent decompositions of identity. If E is a categorical idempotent then End(E) is a graded commutative algebra. The same is true of Hom(E,Eᶜ[1]) under certain circumstances, where Eᶜ is the complement. These generalize the notions of cohomology and Tate cohomology of a finite dimensional Hopf algebra, respectively.
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