Operadic categories and decalage
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Batanin and Markl's operadic categories are categories in which each map is endowed with a finite collection of "abstract fibres"-also objects of the same category-subject to suitable axioms. We give a reconstruction of the data and axioms of operadic categories in terms of the decalage comonad Don small categories. A simple case involves unaryoperadic categories-ones wherein each map has exactly one abstract fibre-which are exhibited as categories which are, first of all, coalgebras for the comonad D, and, furthermore, algebras for the monad (D) over tilde induced on Cat(D) by the forgetful-cofree adjunction. A similar description is found for general operadic categories arising out of a corresponding analysis that starts from a "modified decalage" comonad D-m on the arrow category Cat(2). (C) 2020 Elsevier Inc. All rights reserved.
Original language | English |
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Article number | 107440 |
Journal | Advances in Mathematics |
Volume | 377 |
Number of pages | 23 |
ISSN | 0001-8708 |
DOIs | |
Publication status | Published - 22 Jan 2021 |
Externally published | Yes |
- Operadic categories, 2-Segal spaces, Decalage
Research areas
ID: 331497046