Related papers: The Generating Condition for Coalgebras

We prove that a countable dimensional associative algebra (resp. a countable semigroup) of locally subexponential growth is $M_\infty$-embeddable as a left ideal in a finitely generated algebra (resp. semigroup) of subexponential growth.…

We study certain special tilting and cotilting modules for an algebra with positive dominant dimension, each of which is generated or cogenerated (and usually both) by projective-injectives. These modules have various interesting…

For a ring $R$ and an additive subcategory $\C$ of the category $\Mod R$ of left $R$-modules, under some conditions we prove that the right Gorenstein subcategory of $\Mod R$ and the left Gorenstein subcategory of $\Mod R^{op}$ relative to…

Given a compact, metric space X, we show that the commutative C*-algebra C(X) is semiprojective if and only if X is an absolute neighborhood retract of dimension at most one. This confirms a conjecture of Blackadar. Generalizing to the…

A compact T-algebra is an initial T-algebra whose inverse is a final T-coalgebra. Functors with this property are said to be algebraically compact. This is a very strong property used in programming semantics which allows one to interpret…

Let $A$ be a finite dimensional associative $\mathbb{K}$-algebra over an algebraically closed field $\mathbb{K}$ of characteristic zero. To $A$, we can associate its basic form that is given by a quiver $Q = (Q_0, Q_1)$ with an admissible…

Starting from a comonad G on a category A, and a functor L : B -> A with a right adjoint R : A -> B, we will give a parametrization of the functors K from B to the category of all G-coalgebras that factorize throughout L in terms of…

Although regular conditional distributions (r.c.d.) are well-defined and widely used measure-theoretic objects, they can violate our intuition from the classical definition of a conditional probability given an event. For that purpose, the…

Given a ring $A$ and an $A$-coring $\cC$ we study when the forgetful functor from the category of right $\cC$-comodules to the category of right $A$-modules and its right adjoint $-\otimes_A\cC$ are separable. We then proceed to study when…

We characterize noncommutative Frobenius algebras A in terms of the existence of a coproduct which is a map of left A^e-modules. We show that the category of right (left) comodules over A, relative to this coproduct, is isomorphic to the…

It is shown that if A is a stably finite C*-algebra and E is a countably generated Hilbert A-module, then E gives rise to a compact element of the Cuntz semigroup if and only if E is algebraically finitely generated and projective. It…

This paper is a follow-up to arXiv:2212.09639. We consider two algebraic settings of comodules over a coring and contramodules over a topological ring with a countable base of two-sided ideals. These correspond to two (noncommutative)…

We develop the basic constructions of homological algebra in the (appropriately defined) unbounded derived categories of modules over algebras over coalgebras over noncommutative rings (which we call semialgebras over corings). We define…

We propose a criterion for preserving the regularity of a formal language representation when passing from groups to subgroups. We use this criterion to show that the regularity of a positive cone language in a left-orderable group passes…

Motivated by the classical correspondence between short exact sequences and splitting properties in module theory, this paper examines the projective and injective analogues within the category of Lie algebras. We first show that no Lie…

We give a positive answer to a conjecture of Faith stating that a self-injective semiprimary ring is QF, for algebras which are at most countable dimensional modulo their Jacobson radical. As a consequence of the method used, we also give…

We give natural descriptions of the homology and cohomology algebras of regular quotient ring spectra of even E-infinity ring spectra. We show that the homology is a Clifford algebra with respect to a certain bilinear form naturally…

In their previous work, S. Koenig, S. Ovsienko and the second author showed that every quasi-hereditary algebra is Morita equivalent to the right algebra, i.e. the opposite algebra of the left dual, of a coring. Let $A$ be an associative…

We introduce the quiver of a bicomodule over a cosemisimple coalgebra. Applying this to the coradical $C_0$ of an arbitrary coalgebra $C$, we give an alternative definition of the Gabriel quiver of $C$, and then show that it coincides with…

We show under mild hypotheses that a Quillen adjunction between stable model categories induces another Quillen adjunction between their left localizations, and we provide conditions under which the localized adjunction is a Quillen…