Idempotents in triangulated monoidal categories
Category Theory
2017-03-06 v1
Abstract
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 is a categorical idempotent then is a graded commutative algebra. The same is true of under certain circumstances, where is the complement. These generalize the notions of cohomology and Tate cohomology of a finite dimensional Hopf algebra, respectively.
Cite
@article{arxiv.1703.01001,
title = {Idempotents in triangulated monoidal categories},
author = {Matthew Hogancamp},
journal= {arXiv preprint arXiv:1703.01001},
year = {2017}
}