Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Idempotents in triangulated monoidal categories   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 $\mathbf{E}$ is a categorical
idempotent then $\operatorname{End}(\mathbf{E})$ is a graded commutative
algebra. The same is true of $\operatorname{Hom}(\mathbf{E},\mathbf{E}^c[1])$
under certain circumstances, where $\mathbf{E}^c$ is the complement. These
generalize the notions of cohomology and Tate cohomology of a finite
dimensional Hopf algebra, respectively.

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The categories of this paper are: eess
30
The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
3
The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat