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COIDEMPOTENT SUBCOALGEBRAS AND SHORT EXACT SEQUENCES OF FINITARY 2-REPRESENTATIONS

Part of: Representation theory of rings and algebras Categories with structure

Published online by Cambridge University Press:  19 March 2020

AARON CHAN Open the ORCID record for AARON CHAN [Opens in a new window]  and
VANESSA MIEMIETZ
AARON CHAN
Affiliation:
Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya, Japan email [email protected]
VANESSA MIEMIETZ
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK email [email protected]
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Abstract

In this article, we study short exact sequences of finitary 2-representations of a weakly fiat 2-category. We provide a correspondence between such short exact sequences with fixed middle term and coidempotent subcoalgebras of a coalgebra 1-morphism defining this middle term. We additionally relate these to recollements of the underlying abelian 2-representations.

MSC classification

Primary: 18D05: Double categories, $2$-categories, bicategories and generalizations 16G10: Representations of Artinian rings
Type
Article
Information
Nagoya Mathematical Journal , Volume 243 , September 2021 , pp. 316 - 341
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Copyright
© 2020 Foundation Nagoya Mathematical Journal

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