Displaying similar documents to “Finitely presentable morphisms in exact sequences.”

Finitely silting comodules in quasi-finite comodule category

Qianqian Yuan, Hailou Yao (2023)

Czechoslovak Mathematical Journal

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We introduce the notions of silting comodules and finitely silting comodules in quasi-finite category, and study some properties of them. We investigate the torsion pair and dualities which are related to finitely silting comodules, and give the equivalences among silting comodules, finitely silting comodules, tilting comodules and finitely tilting comodules.

Finite presentation and purity in categories σ[M]

Mike Prest, Robert Wisbauer (2004)

Colloquium Mathematicae

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For any module M over an associative ring R, let σ[M] denote the smallest Grothendieck subcategory of Mod-R containing M. If σ[M] is locally finitely presented the notions of purity and pure injectivity are defined in σ[M]. In this paper the relationship between these notions and the corresponding notions defined in Mod-R is investigated, and the connection between the resulting Ziegler spectra is discussed. An example is given of an M such that σ[M] does not contain any non-zero finitely...

On von Neumann varieties.

Borceux, F., Rosický, J. (2004)

Theory and Applications of Categories [electronic only]

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On pure quotients and pure subobjects

Jiří Adámek, Jiří Rosický (2004)

Czechoslovak Mathematical Journal

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In the theory of accessible categories, pure subobjects, i.e. filtered colimits of split monomorphisms, play an important role. Here we investigate pure quotients, i.e., filtered colimits of split epimorphisms. For example, in abelian, finitely accessible categories, these are precisely the cokernels of pure subobjects, and pure subobjects are precisely the kernels of pure quotients.