#
An embedding theorem for adhesive categories

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Stephen Lack

Adhesive categories are categories which have pushouts with one leg a
monomorphism, all pullbacks, and certain exactness conditions relating these
pushouts and pullbacks. We give a new proof of the fact that every topos is
adhesive. We also prove a converse: every small adhesive category has a fully
faithful functor in a topos, with the functor preserving the all the structure.
Combining these two results, we see that the exactness conditions in the
definition of adhesive category are exactly the relationship between pushouts
along monomorphisms and pullbacks which hold in any topos.

Keywords:
adhesive category, topos, embedding theorem

2000 MSC:
18A30, 18B15, 18B25

*Theory and Applications of Categories,*
Vol. 25, 2011,
No. 7, pp 180-188.

Published 2011-03-10.

http://www.tac.mta.ca/tac/volumes/25/7/25-07.dvi

http://www.tac.mta.ca/tac/volumes/25/7/25-07.ps

http://www.tac.mta.ca/tac/volumes/25/7/25-07.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/25/7/25-07.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/25/7/25-07.ps

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