相关论文: Isomorphisms between left and right adjoints
There appeared not long ago a Reduction Formula for derived Hochschild cohomology, that has been useful e.g., in the study of Gorenstein maps and of rigidity w.r.t. semidualizing complexes. The formula involves the relative dualizing…
We give a structural characterisation of linear operators from one $C^\ast$% -algebra into another whose adjoints map extreme points of the dual ball onto extreme points. We show that up to a $\ast$-isomorphism, such a map admits of a…
We define, for a somewhat standard forgetful functor from nonsymmetric operads to weight graded associative algebras, two functorial "enveloping operad" functors, the right inverse and the left adjoint of the forgetful functor. Those…
The binary products of right, left or double division in semigroups that are semilattices of groups give interesting groupoid structures that are in one to one correspondence with semigroups that are semilattices of groups. This work is…
All subalgebras, idempotents, left(right) ideals and left quasi-units of two-dimensional algebras are described. Classification of algebras with given number of subalgebras, left(right) ideals are provided. In particular, a list of…
Diers developed a general theory of right multi-adjoint functors leading to a purely categorical, point-set construction of spectra. Situations of multiversal properties return sets of canonical solutions rather than a unique one. In the…
Let $\mathcal{A}$ and $\mathcal{B}$ be monoidal categories and let $R:\mathcal{A} \rightarrow \mathcal{B}$ be a lax monoidal functor. If $R$ has a left adjoint $L$, it is well-known that the two adjoints induce functors $\overline{R}={\sf…
Let E be a (right) Hilbert C*-module over a C*-algebra A. If E is equipped with a left action of a second C*-algebra B, then tensor product with E gives rise to a functor from the category of Hilbert B-modules to the category of Hilbert…
In this paper, we construct a bialgebraic and further a Hopf algebraic structure on top of subgraphs of a given graph. Further, we give the dual structure of this Hopf algebraic structure. We study the algebra morphisms induced by graph…
In this paper we describe all, up to isomorphism, left unital, right unital and unital algebra structures on two-dimensional vector space over any algebraically closed field and $\mathbb{R}$. We tabulate the algebras with the units.
To determine that two given undirected graphs are isomorphic, we construct for them auxiliary graphs, using the breadth-first search. This makes capability to position vertices in each digraph with respect to each other. If the given graphs…
The new notion of adjoint algebraic entropy of endomorphisms of Abelian groups is introduced. Various examples and basic properties are provided. It is proved that the adjoint algebraic entropy of an endomorphism equals the algebraic…
We present two results on the relation between the class of right regular bands (RRBs) and their underlying *associative posets*. The first one is a construction of a left adjoint to the forgetful functor that takes an RRB $(P,\cdot)$ to…
A classical result of topological algebra states that any compact left topological semigroup has an idempotent. We refine this by showing that any compact left topological left semiring has a common, i.e. additive and multiplicative…
It is known that the so-called monadic decomposition, applied to the adjunction connecting the category of bialgebras to the category of vector spaces via the tensor and the primitive functors, returns the usual adjunction between…
This contribution studies a specific deformation of algebras with anti-involution. Starting with the observation that twisting the multiplication of such an algebra by its anti-involution generates a Hom-associative algebra of type II, it…
We give a construction of triangulated categories as quotients of exact categories where the subclass of objects sent to zero is defined by a triple of functors. This includes the cases of homotopy and stable module categories. These…
Given locally compact quantum groups $\G_1$ and $\G_2$, we show that if the convolution algebras $L^1(\G_1)$ and $L^1(\G_2)$ are isometrically isomorphic as algebras, then $\G_1$ is isomorphic either to $\G_2$ or the commutant $\G_2'$.…
In this short note, we construct a right adjoint to the functor which associates to a ring $R$ equipped with a group action its twisted group ring. This right adjoint admits an interpretation as semilinearization, in that it sends an…
By Rickard's work, two rings are derived equivalent if there is a tilting complex, constructed from projective modules over the first ring such that the second ring is the endomorphism ring of this tilting complex. In this work I describe,…