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Categories enriched over a quantaloid: Isbell adjunctions and Kan
adjunctions

##
Lili Shen and Dexue Zhang

Each distributor between categories enriched over a small quantaloid
Q gives rise to two adjunctions between the categories of
contravariant and covariant presheaves, and hence to two monads. These
two adjunctions are respectively generalizations of Isbell adjunctions
and Kan extensions in category theory. It is proved that these two
processes are functorial with infomorphisms playing as morphisms
between distributors; and that the free cocompletion functor of
Q-categories factors through both of these functors.

Keywords:
Quantaloid, Q-distributor, complete Q-category,
Q-closure space, Isbell adjunction, Kan adjunction

2010 MSC:
18A40, 18D20

*Theory and Applications of Categories,*
Vol. 28, 2013,
No. 20, pp 577-615.

Published 2013-07-21.

http://www.tac.mta.ca/tac/volumes/28/20/28-20.dvi

http://www.tac.mta.ca/tac/volumes/28/20/28-20.ps

http://www.tac.mta.ca/tac/volumes/28/20/28-20.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/28/20/28-20.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/28/20/28-20.ps

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