Journal Article10.1007/S00012-006-1977-X
Purity in algebra
Francis Borceux,Jirí Rosický +1 more
16
TL;DR: In this article, pure monomorphisms and pure epimorphisms in universal algebras with applications to equationally compact, pure injective, and pure projective algesbras are investigated.
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Abstract: We investigate pure monomorphisms and pure epimorphisms in varieties of universal algebras with applications to equationally compact (= pure injective) algebras, pure projective algebras and perfect varieties.
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Citations
Pure-injective modules
Mike Prest
- 27 Sep 2008
TL;DR: A survey of pure-injective modules can be found in this article, where the authors present and illustrate the definitions and a number of the results around the notion of pure embeddings.
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Accessible aspects of 2-category theory
TL;DR: In this paper, it was shown that if the categorical structure in question is sufficiently weak (such as the structure of monoidal but not strict monoidal, categories) then the 2-category in question was accessible.
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Weak factorization systems and stable independence
Michael Lieberman,Jiří Rosický,Sebastien Vasey +2 more
- 11 Apr 2019
TL;DR: In this article, a bridge between the theory of cellular categories, used in algebraic topology and homological algebra, and the model-theoretic notion of stable independence is constructed.
12
Cofibrant generation of pure monomorphisms
TL;DR: In this article, it was shown that pure monomorphisms are cofibrantly generated from a set of morphisms by pushouts, transfinite composition, and retracts in any locally finitely presentable additive category.
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•Posted Content
Cellular categories and stable independence
TL;DR: In this article, a bridge between the theory of cellular categories, used in algebraic topology and homological algebra, and the model-theoretic notion of stable independence is constructed.
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References
Handbook of Categorical Algebra
Francis Borceux
- 26 Aug 1994
TL;DR: The Handbook of Categorical Algebra is intended to give, in three volumes, a rather detailed account of what, ideally, everybody working in category theory should know, whatever the specific topic of research they have chosen.
1.4K
•Book
Locally presentable and accessible categories
Jirí Adámek,Jiri Rosicky +1 more
- 01 Jan 1994
TL;DR: The concepts of locally presentable categories and an accessible category have turned out to be extremely useful in creating connections between universal algebra, model-theory, logic and computer science as discussed by the authors.
1.2K
Finitistic dimension and a homological generalization of semi-primary rings
TL;DR: In this article, Kaplansky showed that a commutative ring R is left T-nilpotent if, given any sequence {at} of elements in N, there exists an re such that ai • • • an = 0.