Categories of weak fractions
(2019) Theory and Applications of Categories — Vol. 34, n° 46, p. 1526-1551 (2019)
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- Authors
Jacqmin, Pierre-Alain 
- Abstract
- Given a set Σ of morphisms in a category C, we construct a functor F_{1/Σ} : C → C[1/Σ] which sends elements of Σ to split monomorphisms. Moreover, we prove that F_{1/Σ} 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 Σ into the existence of some kind of weak right adjoint for F_{1/Σ}.
- Affiliations
University of Ottawa Department of Mathematics and Statistics
Citations
Jacqmin, P.-A. (2019). Categories of weak fractions. Theory and Applications of Categories, 34(46), 1526-1551. https://hdl.handle.net/2078.5/122294 (Original work published 2019)