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Recollements, comma categories and morphic enhancements

Part of: General theory of categories and functors Abelian categories

Published online by Cambridge University Press:  09 March 2021

Xiao-Wu Chen  and
Jue Le
Xiao-Wu Chen
Affiliation:
Key Laboratory of Wu Wen-Tsun Mathematics, Chinese Academy of Sciences, School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, Anhui, PR China ([email protected], [email protected])
Jue Le
Affiliation:
Key Laboratory of Wu Wen-Tsun Mathematics, Chinese Academy of Sciences, School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, Anhui, PR China ([email protected], [email protected])
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Abstract

For each recollement of triangulated categories, there is an epivalence between the middle category and the comma category associated with a triangle functor from the category on the right to the category on the left. For a morphic enhancement of a triangulated category $\mathcal {T}$, there are three explicit ideals of the enhancing category, whose corresponding factor categories are all equivalent to the module category over $\mathcal {T}$. Examples related to inflation categories and weighted projective lines are discussed.

Keywords

Recollementcomma categorymorphic enhancementsubmodule categoryweighted projective line

MSC classification

Primary: 18E30: Derived categories, triangulated categories
Secondary: 18A25: Functor categories, comma categories 18E10: Exact categories, abelian categories
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 152 , Issue 3 , June 2022 , pp. 567 - 591
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Copyright
Copyright © The Author(s) 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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