| Title:
|
Finite duals in Grothendieck categories and coalgebra objects (English) |
| Author:
|
Banerjee, Abhishek |
| Author:
|
Kour, Surjeet |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
8 |
| Issue:
|
1 |
| Year:
|
2024 |
| Pages:
|
224-243 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We develop a theory of coalgebra objects and comodules that is internal to any $k$-linear Grothendieck category, where $k$ is a commutative noetherian ring. We begin with a counterpart in $k$-linear Grothendieck categories for the finite dual construction of a $k$-algebra and the comodules over it. In the second part of the paper, we construct "coalgebra objects" inside a Grothendieck category. These are not coalgebras in an explicit sense, but enjoy several categorical properties arising in the classical theory of coalgebras, such as those of semiperfect or quasi-co-Frobenius coalgebras. In particular, this construction works in any Grothendieck category and there is no need for a monoidal structure in order to define these coalgebra objects. (English) |
| Keyword:
|
coalgebra objects |
| Keyword:
|
Grothendieck categories |
| MSC:
|
16D50 |
| MSC:
|
16T15 |
| MSC:
|
18E10 |
| idZBL:
|
Zbl 1558.16006 |
| idMR:
|
MR4752521 |
| DOI:
|
10.21136/HS.2024.05 |
| . |
| Date available:
|
2026-03-13T14:08:39Z |
| Last updated:
|
2026-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153469 |
| . |
| Reference:
|
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