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Duality in non-abelian algebra I. From cover relations to Grandis ex2-categories
Theory and applications of categories, Tome 29 (2014), pp. 315-331 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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.

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Classification : 18D30, 18A32, 18A20, 18E10, 18G50, 06A15, 06A75, 06F99
Keywords: biform, cover relation, ex2-category, factorization system, faithful amnestic functor, form, Grothendieck fibration, ideal of null morphisms, subobject, universalizer 
@article{TAC_2014_29_a10,
     author = {Zurab Janelidze and Thomas Weighill},
     title = {Duality in non-abelian algebra {I.} {From} cover relations to {Grandis} 
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     journal = {Theory and applications of categories},
     pages = {315--331},
     year = {2014},
     volume = {29},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2014_29_a10/}
}
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ex2-categories
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Zurab Janelidze; Thomas Weighill. Duality in non-abelian algebra I. From cover relations to Grandis 
ex2-categories. Theory and applications of categories, Tome 29 (2014), pp. 315-331. http://geodesic.mathdoc.fr/item/TAC_2014_29_a10/