#
Duality in non-abelian algebra I. From cover relations to Grandis
ex2-categories

##
Zurab Janelidze and Thomas Weighill

The aim of this series of papers is to develop a self-dual categorical
approach to some topics in non-abelian algebra, which is based on
replacing the framework of a category with that of a category equipped
with a functor to it. The present paper gives some preliminary steps in
this direction, where several known structures on a category, which arise
in the categorical treatment of these topics, are viewed as such functors;
as a result, we obtain some new conceptual links between these structures.

Keywords:
biform, cover relation, ex2-category, factorization system, faithful
amnestic functor,
form, Grothendieck fibration, ideal of null morphisms, subobject,
universalizer

2010 MSC:
18D30, 18A32, 18A20, 18E10, 18G50, 06A15, 06A75, 06F99

*Theory and Applications of Categories,*
Vol. 29, 2014,
No. 11, pp 315-331.

Published 2014-06-18.

http://www.tac.mta.ca/tac/volumes/29/11/29-11.pdf

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