5 research outputs found
Some remarks on connectors and groupoids in goursat categories
We prove that connectors are stable under quotients in any (regular) Goursat category. As a consequence, the category Conn(C) of connectors in C is a Goursat category whenever C is. This implies that Goursat categories can be characterised in terms of a simple property of internal groupoids.Portuguese Government through FCT/MCTES; European Regional Development Fun
A new characterisation of Goursat categories
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 existence of the quaternary operations characterising 3-permutable varieties
A new characterization of Goursat categories
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 existence of the quaternary operations
characterising 3-permutable varietie
Relative Goursat categories
We define relative Goursat categories and prove relative versions of the equivalent conditions defining regular Goursat categories. These include 3-permutability of equivalence relations, preservation of equivalence relations under direct images, a condition on so-called Goursat pushouts, and the denormalised 3×3 Lemma. This extends recent work by Gran and Rodelo on a new characterisation of Goursat categories to a relative context. © 2012 Elsevier B.V.