COMMUTATOR THEORY IN STRONGLY PROTOMODULAR CATEGORIES Dedicated to Aurelio Carboni on the occasion of his sixtieth birthday
نویسنده
چکیده
We show that strongly protomodular categories (as the category Gp of groups for instance) provide an appropriate framework in which the commutator of two equivalence relations do coincide with the commutator of their associated normal subobjects, whereas it is not the case in any semi-abelian category.
منابع مشابه
SEMI - ABELIAN MONADIC CATEGORIES Dedicated to Aurelio Carboni on the occasion of his sixtieth birthday . MARINO GRAN AND
We characterize semi-abelian monadic categories and their localizations. These results are then used to obtain a characterization of pointed protomodular quasimonadic categories, and in particular of protomodular quasivarieties.
متن کاملGENERIC MORPHISMS, PARAMETRIC REPRESENTATIONS AND WEAKLY CARTESIAN MONADS Dedicated to Aurelio Carboni on the occasion of his sixtieth birthday
Two notions, generic morphisms and parametric representations, useful for the analysis of endofunctors arising in enumerative combinatorics, higher dimensional category theory, and logic, are defined and examined. Applications to the Batanin approach to higher category theory, Joyal species and operads are provided.
متن کاملON EXTENSIONS OF LAX MONADS Dedicated to Aurelio Carboni on the occasion of his sixtieth birthday
In this paper we construct extensions of Set-monads – and, more generally, of lax Rel-monads – into lax monads of the bicategory Mat(V) of generalized V-matrices, whenever V is a well-behaved lattice equipped with a tensor product. We add some guiding examples.
متن کاملON VON NEUMANN VARIETIES To Aurelio Carboni , on his sixtieth birthday
We generalize to an arbitrary variety the von Neumann axiom for a ring. We study its implications on the purity of monomorphisms and the flatness of algebras.
متن کاملTHE MONOIDAL CENTRE AS A LIMIT To Aurelio Carboni for his sixtieth birthday
The centre of a monoidal category is a braided monoidal category. Monoidal categories are monoidal objects (or pseudomonoids) in the monoidal bicategory of categories. This paper provides a universal construction in a braided monoidal bicategory that produces a braided monoidal object from any monoidal object. Some properties and sufficient conditions for existence of the construction are exami...
متن کامل