Related papers: Epireflections in topological algebraic structures
Let p=tp(a/A) be a stationary type in an arbitrary finite rank stable theory, and P an A-invariant family of partial types. The following property is introduced and characterised: whenever c is definable over (A,a) and a is not algebraic…
It is important for applications of Homological Algebra in Representation Theory to have control over the behaviour of (minimal) projective resolutions under various functors. In this article we describe three broad families of functors…
We prove that both, the embedding of the category of Hopf algebras into that of bialgebras and the forgetful functor from the category of Hopf algebras to the category of algebras, have right adjoints; in other words: every bialgebra has a…
We call a finitely complete category algebraically coherent when the change-of-base functors of its fibration of points are coherent, which means that they preserve finite limits and jointly strongly epimorphic pairs of arrows. We give…
We study the locally compact abelian groups in the class $\mathfrak E_{<\infty}$, that is, having only continuous endomorphisms of finite topological entropy, and in its subclass $\mathfrak E_0$, that is, having all continuous endomorphisms…
Some basic features of the simultaneous inclusion of discrete fibrations and discrete opfibrations in categories over a base category X are considered. In particular, we illustrate the formulas (|P)x = ten(x/X,P) ; (P|)x = hom(X/x,P) which…
In this paper, we give a finite number of defining relations satisfied by a finite number of generators for the elliptic Lie algebras and superalgebras ${\frak g}_R$ with rank $\geq 2$. Here the $R$'s denote the reduced and non-reduced…
For separable $C^*$-algebras $A$ and $B$, we define a topology on the set $[[A, B]]$ consisting of homotopy classes of asymptotic morphisms from $A$ to $B$. This gives an enrichment of the Connes--Higson asymptotic category over topological…
A full reflective subcategory E of a presheaf category [C*,Set] is the category of sheaves for a topology j on C if and only if the reflection preserves finite limits. Such an E is called a Grothendieck topos. More generally, one can…
We prove that every topological space (T0-space, T1-space) can be embedded in a pseudoradial space (in a pseudoradial T0-space, T1space). This answers the Problem 3 in [Arhangelskii, A.V. - Isler, R. - Tironi, G: On pseudo-radial spaces,…
In a previous paper [1] [MR4101040], we initiated a systematic study of semihypergroups and had a thorough discussion about some important analytic and algebraic objects associated to this class of objects. In this paper, we investigate…
We explore a curious type of equivalence between certain pairs of reflective and coreflective subcategories. We illustrate with examples involving noncommutative duality for C*-dynamical systems and compact quantum groups, as well as…
Some basic features of the simultaneous inclusion of discrete fibrations and discrete opfibrations on a category A in the category of categories over A are studied; in particular, the reflections and the coreflections of the latter in the…
Modular functors, i.e. consistent systems of projective representations of mapping class groups of surfaces, have been constructed for non-semisimple modular categories already decades ago. Concepts from homological algebra have not been…
Let $S$ be an integral domain with field of fractions $F$ and let $A$ be an $F$-algebra. An $S$-subalgebra $R$ of $A$ is called $S$-nice if $R$ is lying over $S$ and the localization of $R$ with respect to $S \setminus \{ 0 \}$ is $A$. Let…
In this paper we prove an $\infty$-categorical version of the reflection theorem of Ad\'amek-Rosick\'y. Namely, that a full subcategory of a presentable $\infty$-category which is closed under limits and $\kappa$-filtered colimits is a…
When working with (multi-parameter) persistence modules, one usually makes some type of tameness assumption in order to obtain better control over their algebraic behavior. One such notion is Ezra Millers notion of finite encodability,…
This paper contributes to a theory of the behaviour of "finite-state" systems that is generic in the system type. We propose that such systems are modelled as coalgebras with a finitely generated carrier for an endofunctor on a locally…
This paper contributes to a theory of the behaviour of "finite-state" systems that is generic in the system type. We propose that such systems are modeled as coalgebras with a finitely generated carrier for an endofunctor on a locally…
In this note, we show that the epimorphic subgroups of an algebraic group are exactly the pull-backs of the epimorphic subgroups of its affinization. We also obtain epimorphicity criteria for subgroups of affine algebraic groups, which…