#
Extensions and Glueing in Double Categories

##
Susan Niefield

Let D be a double category with an initial object. Any cotabulator Gamma(v)
of a vertical morphism v:X-->Y gives rise to an extension (i.e., short exact
sequence) X-->Gamma(v)-->Y in the vertical bicategory VD. If D has "open
cokernels" then every extension in VD is equivalent to one of this form.
Examples include the double categories Loc, Topos, Pos, and Cat, whose
objects are locales, toposes, posets, and small categories, respectively;
and Gamma(v) is given by Artin-Wraith glueing along v in the first two
cases, and by the collage of v in the others.

Keywords:
double categories, extensions, glueing, locales, toposes, posets, profunctors

2020 MSC:
18N10, 20E22, 18B25, 06D22, 18F70, 18D60, 18B35

*Theory and Applications of Categories,*
Vol. 36, 2021,
No. 13, pp 348-367.

Published 2021-06-02.

http://www.tac.mta.ca/tac/volumes/36/13/36-13.pdf

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