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Titlebook: Mal‘cev, Protomodular, Homological and Semi-Abelian Categories; Francis Borceux,Dominique Bourn Book 2004 Springer Science+Business Media

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d synthetic notions of Mal‘cev, protomodular, homological and semi-abelian categories emerged. These notions force attention on the fibration of points and allow a unified treatment of the main algebraic: homological lemmas, Noether isomorphisms, commutator theory. .The book gives full importance to
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Book 2004knowing an object, not from inside via its elements, but from outside via its relations with its environment. .The book is intended to be a powerful tool in the hands of researchers in category theory, homology theory and universal algebra, as well as a textbook for graduate courses on these topics.
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raint is: knowing an object, not from inside via its elements, but from outside via its relations with its environment. .The book is intended to be a powerful tool in the hands of researchers in category theory, homology theory and universal algebra, as well as a textbook for graduate courses on these topics.978-90-481-6551-3978-1-4020-1962-3
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Metatheorems,, with the category of modules on a ring as reference, and the toposes, with the category of sets as reference, are the most celebrated examples to this respect. This preliminary chapter introduces — or recalls — two rather elementary such metatheorems which, in this book, will frequently provide the quickest way to prove results.
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Book 2004c notions of Mal‘cev, protomodular, homological and semi-abelian categories emerged. These notions force attention on the fibration of points and allow a unified treatment of the main algebraic: homological lemmas, Noether isomorphisms, commutator theory. .The book gives full importance to examples
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Metatheorems,gory, the statement holds more generally in a wide collection of abstract categories satisfying a given set of axioms. The cases of abelian categories, with the category of modules on a ring as reference, and the toposes, with the category of sets as reference, are the most celebrated examples to th
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