Diana Rodelo

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We present a new characterisation of Goursat categories in terms of special kind of pushouts, that we call Goursat pushouts. This allows one to prove that, for a regular category, the Goursat property is actually equivalent to the validity of the denormalised 3-by-3 Lemma. Goursat pushouts are also useful to clarify, from a categorical perspective, the(More)
We show that varietal techniques based on the existence of operations of a certain arity can be extended to n-permutable categories with binary coproducts. This is achieved via what we call approximate Hagemann– Mitschke co-operations, a generalisation of the notion of approximate Mal'tsev cooperation [2]. In particular, we extend characterisation theorems(More)
A new method for realizing the first and second order cohomology groups of an internal abelian group in a Barr-exact category was introduced in [6] and [10]. The main role, in each level, is played by a direction functor. This approach can be generalized to any level n and produces a long exact cohomology sequence. By applying this method to Moore(More)
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