#
Adjunction up to automorphism

##
D. Tambara

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.

Keywords:
distributor, adjoint, nearly representable

2010 MSC:
18A40

*Theory and Applications of Categories,*
Vol. 34, 2019,
No. 31, pp 993-1035.

Published 2019-10-03.

http://www.tac.mta.ca/tac/volumes/34/31/34-31.pdf

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