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Hereditarity of closure operators and injectivity

Gabriele Castellini, Eraldo Giuli (1992)

Commentationes Mathematicae Universitatis Carolinae

A notion of hereditarity of a closure operator with respect to a class of monomorphisms is introduced. Let C be a regular closure operator induced by a subcategory 𝒜 . It is shown that, if every object of 𝒜 is a subobject of an 𝒜 -object which is injective with respect to a given class of monomorphisms, then the closure operator C is hereditary with respect to that class of monomorphisms.

Higher monodromy.

Polesello, Pietro, Waschkies, Ingo (2005)

Homology, Homotopy and Applications

Higher-dimensional Auslander-Reiten sequences

Jiangsha Li, Jing He (2024)

Czechoslovak Mathematical Journal

Zhou and Zhu have shown that if 𝒞 is an ( n + 2 ) -angulated category and 𝒳 is a cluster tilting subcategory of 𝒞 , then the quotient category 𝒞 / 𝒳 is an n -abelian category. We show that if 𝒞 has Auslander-Reiten ( n + 2 ) -angles, then 𝒞 / 𝒳 has Auslander-Reiten n -exact sequences.

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