Comodules and contramodules over coalgebras associated with locally finite categories · arXivDesk
2307.13358Jul 25, 2023LaTeX 2e with xy-pic; 35 pages, 1 commutative diagram; v.2: Question 4.12 added, new Section 6 inserted; v.3: misprints corrected, proof of Theorem 3.7 reworked with Lemma 3.8 created, a paragraph inserted in the introduction, Examples 7.6 added at the end
Comodules and contramodules over coalgebras associated with locally finite categories
We explain how to attach a coalgebra C over a field k to a small k-linear category E satisfying suitable finiteness conditions. In this context, we study full-and-faithfulness of the contramodule forgetful functor, and describe explicitly the categories of locally finite left C-comodules and left C
Nearby in the stack
-contramodules as certain full subcategories of the category of left
E
-modules.
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