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Drummond Cole, Gabriel C
기하학 수리물리 연구단
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Representations are adjoint to endomorphisms

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Title
Representations are adjoint to endomorphisms
Author(s)
Gabriel C. Drummond-Cole; Hirsh, J; Damien Lejay
Publication Date
2020-06
Journal
JOURNAL OF HOMOTOPY AND RELATED STRUCTURES, v.15, no.2, pp.395 - 395
Publisher
SPRINGER HEIDELBERG
Abstract
© Tbilisi Centre for Mathematical Sciences 2019. The functor that takes a ring to its category of modules has an adjoint if one remembers the forgetful functor to abelian groups: the endomorphism ring of linear natural transformations. This uses the self-enrichment of the category of abelian groups. If one considers enrichments into symmetric sequences or even bisymmetric sequences, one can produce an endomorphism operad or an endomorphism properad. In this note, we show that more generally, given a category C enriched in a monoidal category V, the functor that associates to a monoid in V its category of representations in C is adjoint to the functor that computes the endomorphism monoid of any functor with domain C. After describing the first results of the theory we give several examples of applications.
URI
https://pr.ibs.re.kr/handle/8788114/8973
DOI
10.1007/s40062-020-00253-5
ISSN
2193-8407
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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