Related papers: Rota-Baxter Categories
In this paper we apply the methods of rewriting systems and Gr\"obner-Shirshov bases to give a unified approach to a class of linear operators on associative algebras. These operators resemble the classic Rota-Baxter operator, and they are…
Using the language of operated algebras, we construct and investigate a class of operator rings and enriched modules induced by a derivation or Rota-Baxter operator. In applying the general framework to univariate polynomials, one is led to…
We introduce a notion of globular multicategory with homomorphism types. These structures arise when organizing collections of "higher category-like" objects such as type theories with identity types. We show how these globular…
We consider limits over categories of extensions and show how certain well-known functors on the category of groups turn out as such limits. We also discuss higher (or derived) limits over categories of extensions.
We generalize the notion of a Rota-Baxter operator on groups and the notion of a Rota-Baxter operator of weight 1 on Lie algebras and define and study the notion of a Rota-Baxter operator on a cocommutative Hopf algebra $H$. If $H=F[G]$ is…
We prove the well-definedness of some deformations of the fibred biset category in characteristic zero. The method is to realize the fibred biset category and the deformations as the invariant parts of some categories whose compositions are…
We provide a general definition of Toda brackets in a pointed model categories, show how they serve as obstructions to rectification, and explain their relation to the classical stable operations.
We review several known categorification procedures, and introduce a functorial categorification of group extensions with applications to non-abelian group cohomology. Categorification of acyclic models and of topological spaces are briefly…
We examine the use of classes to formulate several categorical notions. This leads to two proposals: an explicit structure for working with subobjects, and a hierarchy of $k$-classes. We apply the latter to both ordinary and higher…
We introduce the Pythagorean C*-algebras and use the category/functor method to construct unitary representations of Thompson's groups from representations of them. We calculate several examples.
We define and give axioms for Garside and locally Garside categories. We give an application to Coxeter and Artin groups and Deligne-Lusztig varieties.
We count the number of all Rota-Baxter operators on a finite direct sum $A = F\oplus F\oplus \ldots \oplus F$ of fields and count all of them up to conjugation with an automorphism. We also study Rota-Baxter operators on $A$ corresponding…
We provide direct inductive constructions of the orientals and the cubes, exhibiting them as the iterated cones, respectively, the iterated cylinders, of the terminal strict globular omega-category.
We find connection between relative Rota--Baxter operators and usual Rota--Baxter operators. We prove that any relative Rota--Baxter operator on a group $H$ with respect to $(G, \Psi)$ defines a Rota--Baxter operator on the semi-direct…
Two new matrix classes are introduced; inverse cyclic matrices and bi-diagonal south-west matrices. An interesting relation is established between these classes. Applications to two classes of inverse $Z$-matrices are provided.
We introduce a notion of a filtered model structure and use this notion to produce various model structures on pro-categories. This framework generalizes several known examples. We give several examples, including a homotopy theory for…
In a triangulated category T with a pair of triangulated subcategories X and Y, one may consider the subcategory of extensions X*Y. We give conditions for X*Y to be triangulated and use them to provide tools for constructing stable…
In this paper, using extension theory and cohomological approach we introduce the notion of the obstruction class for an inner post-Lie algebra being induced by a Rota-Baxter operator, and show that an inner post-Lie algebra is induced by a…
We construct Toda brackets in unstable motivic homotopy theory and prove some fundamental properties of them. Furthermore we construct some examples of motivic Toda brackets.
In this paper we introduce and study motives for rational homotopy types.