Relative Goursat categories
نویسندگان
چکیده
منابع مشابه
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 cha...
متن کاملOn closure operators, reflections and protolocalisations in Goursat categories
By defining a closure operator on effective equivalence relations in a regular category C, it is possible to establish a bijective correspondence between these closure operators and the regular epireflective subcategories of C, on the model of the closure operators on kernels in homological categories [5]. When C is an exact Goursat category [6], this correspondence restricts to a bijection bet...
متن کاملDescent for Regular Epimorphisms in Barr Exact Goursat Categories
We show that the category of regular epimorphisms in a Barr exact Goursat category is almost Barr exact in the sense that (it is a regular category and) every regular epimorphism in it is an effective descent morphism.
متن کاملRelative Mal’tsev Categories
We define relative regular Mal’tsev categories and give an overview of conditions which are equivalent to the relative Mal’tsev axiom. These include conditions on relations as well as conditions on simplicial objects. We also give various examples and counterexamples.
متن کاملRelative Homological Categories
We introduce relative homological and weakly homological categories (C,E), where “relative” refers to a distinguished class E of normal epimorphisms in C. It is a generalization of homological categories, but also protomodular categories can be regarded as examples. We indicate that the relative versions of various homological lemmas can be proved in a relative homological category.
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2012
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2012.02.012