#
Simultaneously Reflective And Coreflective Subcategories of Presheaves

##
Robert El Bashir and Jiri Velebil

It is proved that any category $\cal{K}$ which is equivalent
to a simultaneously reflective and coreflective full subcategory
of presheaves $[\cal{A}^{op},Set]$, is itself equivalent
to the category of the form $[\cal{B}^{op},Set]$ and the inclusion
is induced by a functor $\cal{A} \to \cal{B}$ which
is surjective on objects. We obtain a characterization
of such functors.

Moreover, the base category $Set$ can be replaced with any
symmetric monoidal closed category $V$ which is complete
and cocomplete, and then analogy of the above result holds
if we replace categories by $V$-categories and functors by
$V$-functors.

As a consequence we are able to derive well-known results
on simultaneously reflective and coreflective categories
of sets, Abelian groups, etc.

Keywords: monoidal category, reflection, coreflection, Morita equivalence.

2000 MSC: 18D20, 18A40.

*Theory and Applications of Categories*, Vol. 10, 2002, No. 16, pp 410-423.

http://www.tac.mta.ca/tac/volumes/10/16/10-16.dvi

http://www.tac.mta.ca/tac/volumes/10/16/10-16.ps

http://www.tac.mta.ca/tac/volumes/10/16/10-16.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/10/16/10-16.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/10/16/10-16.ps

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