Geodesic
Categories of weak fractions
Theory and applications of categories, Tome 34 (2019), pp. 1526-1551.

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Given a set $\Sigma$ of morphisms in a category C, we construct a functor F which sends elements of $\Sigma$ to split monomorphisms. Moreover, we prove that F is weakly universal with that property when considered in the world of locally posetal 2-categories. Besides, we also use locally posetal 2-categories in order to construct weak left adjoints to those functors for which any object in the codomain admits a weak reflection. We then apply these two results in order to restate the Injective Subcategory Problem for $\Sigma$ into the existence of some kind of weak right adjoint for F.
Publié le :
Classification : 55P60, 18A40, 18G05 (primary), 18A20, 18D05, 18B35, 18A10 (secondary)
Keywords: split monomorphism, locally posetal 2-category, category of fractions, weak reflection, weak adjoint, injective subcategory problem 
@article{TAC_2019_34_a45,
     author = {Pierre-Alain Jacqmin},
     title = {Categories of weak fractions},
     journal = {Theory and applications of categories},
     pages = {1526--1551},
     publisher = {mathdoc},
     volume = {34},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2019_34_a45/}
}
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Pierre-Alain Jacqmin. Categories of weak fractions. Theory and applications of categories, Tome 34 (2019), pp. 1526-1551. http://geodesic.mathdoc.fr/item/TAC_2019_34_a45/