#
Yoneda representations of flat functors and classifying toposes

##
Olivia Caramello

We obtain semantic characterizations, holding for any Grothendieck
site $(C, J)$, for the models of a theory classified by a
topos of the form $Sh(C,J)$ in terms of the models of a
theory classified by a topos $[C^{op}, Set]$. These
characterizations arise from an appropriate representation of flat
functors into Grothendieck toposes based on an application of the
Yoneda Lemma in conjunction with ideas from indexed category theory,
and turn out to be relevant also in different contexts, in particular
for addressing questions in classical Model Theory.

Keywords:
Classifying topos, Yoneda lemma, flat functor, theory of presheaf type

2010 MSC:
03G30, 18C10, 18B25

*Theory and Applications of Categories,*
Vol. 26, 2012,
No. 21, pp 538-553.

Published 2012-10-12.

http://www.tac.mta.ca/tac/volumes/26/21/26-21.dvi

http://www.tac.mta.ca/tac/volumes/26/21/26-21.ps

http://www.tac.mta.ca/tac/volumes/26/21/26-21.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/26/21/26-21.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/26/21/26-21.ps

TAC Home