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Geiss, Keller and Oppermann (2013) introduced the notion of -angulated category, which is a “higher dimensional” analogue of triangulated category, and showed that certain -cluster tilting subcategories of triangulated categories give rise to -angulated categories. We define mutation pairs in -angulated categories and prove that given such a mutation pair, the corresponding quotient category carries a natural -angulated structure. This result generalizes a theorem of Iyama-Yoshino (2008) for...
Let be a graded ring and an integer. We introduce and study -strongly Gorenstein gr-projective, gr-injective and gr-flat modules. Some examples are given to show that -strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules need not be -strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules whenever . Many properties of the -strongly Gorenstein gr-injective and gr-flat modules are discussed, some known results are generalized. Then we investigate...
In this paper we consider a pair of right adjoint contravariant functors between abelian categories and describe a family of dualities induced by them.
Let be the large source of epimorphisms in the category of Urysohn spaces constructed in [2]. A sink is called natural, if for all . In this paper natural sinks are characterized. As a result it is shown that permits no -factorization structure for arbitrary (large) sources.
In order to facilitate a natural choice for morphisms created by the (left or right) lifting property as used in the definition of weak factorization systems, the notion of natural weak factorization system in the category is introduced, as a pair (comonad, monad) over . The link with existing notions in terms of morphism classes is given via the respective Eilenberg–Moore categories.
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