Objets injectifs dans les catégories abéliennes
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On -exact categories
Said Manjra (2019)
Czechoslovak Mathematical Journal
An -exact category is a pair consisting of an additive category and a class of sequences with terms satisfying certain axioms. We introduce -weakly idempotent complete categories. Then we prove that an additive -weakly idempotent complete category together with the class of all contractible sequences with terms is an -exact category. Some properties of the class are also discussed.
On pure quotients and pure subobjects
Jiří Adámek, Jiří Rosický (2004)
Czechoslovak Mathematical Journal
In the theory of accessible categories, pure subobjects, i.e. filtered colimits of split monomorphisms, play an important role. Here we investigate pure quotients, i.e., filtered colimits of split epimorphisms. For example, in abelian, finitely accessible categories, these are precisely the cokernels of pure subobjects, and pure subobjects are precisely the kernels of pure quotients.
On the categorical foundations of homological and homotopical algebra
Marco Grandis (1992)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
On three types of simplicial objects
S. Balcerzyk, Phan Chan, R. Kiełpiński (1976)
Fundamenta Mathematicae
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