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Orientador(es)
Resumo(s)
Through abelian categories, homological lemmas for modules admit a self-dual treatment, where half of the proof of a lemma is sufficient to prove the full lemma. In this paper we show how the context of a ‘noetherian form’, recently introduced by the second and third authors, allows a self-dual treatment of these lemmas even in the case of non-abelian categories of group-like structures. This context covers a wide range of examples: module categories, the category of groups, of graded abelian groups, the categories of Lie algebras, of cocommutative Hopf algebras, the category of Heyting semilattices, of loops, the dual of the category of pointed sets, the category of modular/distributive lattices and modular connections, the category of sets and partial bijections, and many others. More generally, it includes all semi-abelian and Grandis exact categories.
Descrição
Palavras-chave
3 × 3 Lemma Diagram lemma Dragon lemma Five lemma Group-like structure Goursat’s lemma Homomorphism induction Noetherian form Semi-abelian category Salamander lemma Słominski algebra Snail lemma Snake lemma Spider lemma Weak four lemma
Contexto Educativo
Citação
Editora
Springer