#
Elementary quotient completion

##
Maria Emilia Maietti and Giuseppe Rosolini

We extend the notion of exact completion on a category with weak
finite limits to Lawvere's elementary doctrines. We show how any
such doctrine admits an elementary quotient completion, which is the
universal solution to adding certain quotients. We note that the
elementary quotient completion can be obtained as the composite of two
other universal constructions: one adds effective quotients, the
other forces extensionality of morphisms. We also prove that each
construction preserves comprehension.

Keywords:
quotient completion, split fibration, universal construction

2010 MSC:
03G30 03B15 18C50 03B20 03F55

*Theory and Applications of Categories,*
Vol. 27, 2013,
No. 17, pp 445-463.

Published 2013-09-08

http://www.tac.mta.ca/tac/volumes/27/17/27-17.dvi

http://www.tac.mta.ca/tac/volumes/27/17/27-17.ps

http://www.tac.mta.ca/tac/volumes/27/17/27-17.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/27/17/27-17.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/27/17/27-17.ps

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