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RTA
2015
Springer

Presenting a Category Modulo a Rewriting System

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Presenting a Category Modulo a Rewriting System
Presentations of categories are a well-known algebraic tool to provide descriptions of categories by the means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations where the objects are considered modulo an equivalence relation (in the spirit of rewriting modulo), which is described by equational genWhen those form a convergent (abstract) rewriting system on objects, there are three very natural constructions that can be used to define the category which is described by the presentation: one is based on restricting to objects which are normal forms, one consists in turning equational generators into identities (i.e. considering a quotient category), and one consists in formally adding inverses to equational generators (i.e. localizing the category). We show that, under suitable coherence conditions on the presentation, the three constructions coincide, thus generalizing celebrated results on presentation...
Florence Clerc, Samuel Mimram
Added 17 Apr 2016
Updated 17 Apr 2016
Type Journal
Year 2015
Where RTA
Authors Florence Clerc, Samuel Mimram
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