Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Group actions on categories and Elagin's Theorem Revisited   After recalling basic definitions and constructions for a finite group $G$
action on a $k$-linear category we give a concise proof of the following
theorem of Elagin: if $\mathcal{C} = \langle \mathcal{A}, \mathcal{B} \rangle$
is a semiorthogonal decomposition of a triangulated category which is preserved
by the action of $G$, and $\mathcal{C}^G$ is triangulated, then there is a
semiorthogonal decomposition $\mathcal{C}^G = \langle \mathcal{A}^G,
\mathcal{B}^G \rangle$. We also prove that any $G$-action on $\mathcal{C}$ is
weakly equivalent to a strict $G$-action which is the analog of the Coherence
Theorem for monoidal categories.

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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
3
The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: ao-sci