Geodesic
Adjunction up to automorphism
Theory and applications of categories, Tome 34 (2019), pp. 993-1035 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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We say a set-valued functor on a category is nearly representable if it is a quotient of a representable functor by a group of automorphisms. A distributor is a set-valued functor in two arguments, contravariant in one argument and covariant in the other. We say a distributor is slicewise nearly representable if it is nearly representable in either of the arguments whenever the other argument is fixed. We consider such a distributor a weak analogue of adjunction. Under a finiteness assumption on the domain categories, we show that every slicewise nearly representable functor is a composite of two distributors, each of which may be considered as a weak analogue of (co-)reflective adjunction.

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Classification : 18A40
Keywords: distributor, adjoint, nearly representable 
@article{TAC_2019_34_a30,
     author = {D. Tambara},
     title = {Adjunction up to automorphism},
     journal = {Theory and applications of categories},
     pages = {993--1035},
     year = {2019},
     volume = {34},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2019_34_a30/}
}
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D. Tambara. Adjunction up to automorphism. Theory and applications of categories, Tome 34 (2019), pp. 993-1035. http://geodesic.mathdoc.fr/item/TAC_2019_34_a30/