One example concerning testing categories
One folkloristic lemma on cardinal reflections in Unif
One More Categorical Model of Universal Algebra.
One more remark on reflections
One obstruction for closedness
One-sided Gorenstein subcategories
We introduce the right (left) Gorenstein subcategory relative to an additive subcategory of an abelian category , and prove that the right Gorenstein subcategory is closed under extensions, kernels of epimorphisms, direct summands and finite direct sums. When is self-orthogonal, we give a characterization for objects in , and prove that any object in with finite -projective dimension is isomorphic to a kernel (or a cokernel) of a morphism from an object in with finite -projective dimension...
One-sided -suspended categories
For an integer , we introduce a simultaneous generalization of -exact categories and -angulated categories, referred to as one-sided -suspended categories. Notably, one-sided -angulated categories are specific instances of this structure. We establish a framework for transitioning from these generalized categories to their -angulated counterparts. Additionally, we present a method for constructing -angulated quotient categories from Frobenius -prile categories. Our results unify and extend...
Onto Gelfand maps : appendix
Onto Gelfand transformations
Open covers and infinitary operations in -rings
Open Maps of Toposes.
Opérades différentielles graduées sur les simplexes et les permutoèdres
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 liée aux associaèdres introduite dans un article antérieur.
Operads and algebraic combinatorics of trees.
Operads and algebraic geometry.
Operads and varieties of algebras defined by polylinear identities.
Operads for -ary algebras – calculations and conjectures
In [8] we studied Koszulity of a family of operads depending on a natural number and on the degree of the generating operation. While we proved that, for , the operad is Koszul if and only if is even, and while it follows from [4] that is Koszul for even and arbitrary , the (non)Koszulity of for odd and 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.
Operads in iterated monoidal categories.
Operads of decorated trees and their duals
This is an extended version of a talk presented by the second author on the Third Mile High Conference on Nonassociative Mathematics (August 2013, Denver, CO). The purpose of this paper is twofold. First, we would like to review the technique developed in a series of papers for various classes of di-algebras and show how the same ideas work for tri-algebras. Second, we present a general approach to the definition of pre- and post-algebras which turns out to be equivalent to the construction of dendriform...
Operády v současné matematice