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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 $n \geq 3$ , 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...

Onto Gelfand maps : appendix

Brian J. Day (1989)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Onto Gelfand transformations

B. J. Day (1987)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Open covers and infinitary operations in $C^{\infty}$ -rings

Eduardo J. Dubuc (1981)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Open Maps of Toposes.

Peter T. Johnstone (1980)

Manuscripta mathematica

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 and algebraic combinatorics of trees.

Chapoton, Frédéric (2007)

Séminaire Lotharingien de Combinatoire [electronic only]

Operads and algebraic geometry.

Kapranov, M. (1998)

Documenta Mathematica

Operads and varieties of algebras defined by polylinear identities.

Tronin, S.N. (2006)

Sibirskij Matematicheskij Zhurnal

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 $n \in ℕ$ and on the degree $d \in ℤ$ of the generating operation. While we proved that, for $n \leq 7$ , 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 $n \geq 8$ remains an open problem. In this note we describe some related numerical experiments, and formulate a conjecture suggested by the results of these computations.

Operads in higher-dimensional category theory.

Leinster, Tom (2004)

Theory and Applications of Categories [electronic only]

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