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Colocalization on Grothendieck Categories with Applications to Coalgebras

✍ Scribed by C. Năstăsescu; B. Torrecillas

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
210 KB
Volume
185
Category
Article
ISSN
0021-8693

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✦ Synopsis

We will freely use ''sigma notation'': ⌬ c s Ý c m c for the comulti-1 2 Ž . plication of a coalgebra C and m s Ý m m m for the structure map 0 1 of a right C-comodule M.

Ž . For any abelian category A A we denote Z A A its centre, i.e., the commutative ring of all natural morphisms of the identity functor 1 : A A ª A A.

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Covers and Envelopes in Grothendieck Cat
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✍ S.Tempest Aldrich; Edgar E Enochs; J.R Garcı́a Rozas; Luis Oyonarte 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 136 KB

In the general setting of Grothendieck categories with enough projectives, we prove theorems that make possible to restrict the study of the problem of the existence of -covers and envelopes to the study of some properties of the class . We then prove the existence of flat covers and cotorsion envel