Displaying 301 – 320 of 338

Showing per page

One-sided Gorenstein subcategories

Weiling Song, Tiwei Zhao, Zhaoyong Huang (2020)

Czechoslovak Mathematical Journal

We introduce the right (left) Gorenstein subcategory relative to an additive subcategory 𝒞 of an abelian category 𝒜 , and prove that the right Gorenstein subcategory r 𝒢 ( 𝒞 ) is closed under extensions, kernels of epimorphisms, direct summands and finite direct sums. When 𝒞 is self-orthogonal, we give a characterization for objects in r 𝒢 ( 𝒞 ) , and prove that any object in 𝒜 with finite r 𝒢 ( 𝒞 ) -projective dimension is isomorphic to a kernel (or a cokernel) of a morphism from an object in 𝒜 with finite 𝒞 -projective dimension...

One-sided n -suspended categories

Jing He, Yonggang Hu, Panyue Zhou (2024)

Czechoslovak Mathematical Journal

For an integer n 3 , we introduce a simultaneous generalization of ( n - 2 ) -exact categories and n -angulated categories, referred to as one-sided n -suspended categories. Notably, one-sided n -angulated categories are specific instances of this structure. We establish a framework for transitioning from these generalized categories to their n -angulated counterparts. Additionally, we present a method for constructing n -angulated quotient categories from Frobenius n -prile categories. Our results unify and extend...

Opérades différentielles graduées sur les simplexes et les permutoèdres

Frédéric Chapoton (2002)

Bulletin de la Société Mathématique de France

On définit plusieurs opérades différentielles graduées, dont certaines en relation avec des familles de polytopes : les simplexes et les permutoèdres. On obtient également une présentation de l’opérade K liée aux associaèdres introduite dans un article antérieur.

Operads for n -ary algebras – calculations and conjectures

Martin Markl, Elisabeth Remm (2011)

Archivum Mathematicum

In [8] we studied Koszulity of a family t 𝒜 𝑠𝑠 d n of operads depending on a natural number n and on the degree d of the generating operation. While we proved that, for n 7 , the operad t 𝒜 𝑠𝑠 d n is Koszul if and only if d is even, and while it follows from [4] that t 𝒜 𝑠𝑠 d n is Koszul for d even and arbitrary n , the (non)Koszulity of t 𝒜 𝑠𝑠 d n for d odd and n 8 remains an open problem. In this note we describe some related numerical experiments, and formulate a conjecture suggested by the results of these computations.

Currently displaying 301 – 320 of 338