Related papers: Local theory of almost split sequences for comodul…

We introduce a very general extension of the monomorphism category as studied by Ringel and Schmidmeier which in particular covers generalised species over locally bounded quivers. We prove that analogues of the kernel and cokernel functor…

Let $\mathcal{A}$ be a Hom-finite additive Krull-Schmidt $k$-category where $k$ is an algebraically closed field. Let ${\rm mod} \mathcal{A}$ denote the category of locally finite dimensional $\mathcal{A}$-modules, that is, the category of…

We prove the tame-wild dichotomy conjecture, due to D. Simson, for infinite dimensional algebras and coalgebras. The key part of the approach is proving new representation theoretic characterizations local finiteness. Among other, we show…

Let k be a non archimedean field. If X is a k-algebraic variety and U a locally closed semi-algebraic subset of X^{an} -- the Berkovich space associated to X -- we show that for l \neq char(\tilde{k}), the cohomology groups H^i_c (\bar{U},…

We generalize the "facial weak order" of a finite Coxeter group to a partial order on a set of intervals in a complete lattice. We apply our construction to the lattice of torsion classes of a finite-dimensional algebra and consider its…

In this article, we consider the notion of almost irredundant sets: A subset $\mathcal{X}$ of a C*-algebra $\mathcal{A}$ is called almost irredundant if and only if for every $a\in \mathcal{X}$, the element $a$ does not belong to the…

We continue in this paper the study of locally minimal groups started in \cite{LocMin}. The minimality criterion for dense subgroups of compact groups is extended to local minimality. Using this criterion we characterize the compact abelian…

A locally coherent exact category is a finitely accessible additive category endowed with an exact structure in which the admissible short exact sequences are the directed colimits of admissible short exact sequences of finitely presentable…

We develop axiomatics of highest weight categories and quasi-hereditary algebras in order to incorporate two semi-infinite situations which are in Ringel duality with each other; the underlying posets are either upper finite or lower…

These are the lecture notes for a course at the Summer School on "Applied Analysis" at the Technical University Chemnitz in September 2011. We start with the definition of a fractal algebra and show that the fractal property is enormously…

A deductive system is structurally complete if its admissible inference rules are derivable. For several important systems, like modal logic S5, failure of structural completeness is caused only by the underivability of passive rules, i.e.…

Boolean locales are "almost discrete", in the sense that a spatial Boolean locale is just a discrete locale (that is, it corresponds to the frame of open subsets of a discrete space, namely the powerset of a set). This basic fact, however,…

Under certain integrability and geometric conditions, we prove division theorems for the exact sequences of holomorphic vector bundles and improve the results in the case of Koszul complex. By introducing a singular Hermitian structure on…

Motivated by the structure of the algebras associated to the blocks of the BGG-category O we define a subclass of quasi-hereditary algebras called 1-quasi-hereditary. Many properties of these algebras only depend on the defining partial…

We investigate when the categories of all rational $A$-modules and of finite dimensional rational modules are closed under extensions inside the category of $C^*$-modules, where $C^*$ is the cofinite topological completion of $A$. We give a…

We show that the weak limit of a quasiminimizing sequence is a quasiminimal set. This generalizes the notion of weak limit of a minimizing sequences introduced by De Lellis, De Philippis, De Rosa, Ghiraldin and Maggi. This result is also…

We prove that an embedded cobordism between manifolds with boundary can be split into a sequence of right product and left product cobordisms, if the codimension of the embedding is at least two. This is a topological counterpart of the…

We give a complete list of indecomposable exact module categories over the finite tensor category $\mathrm{Rep}(u_q(\mathfrak{sl}_2))$ of representations of the small quantum group $u_q(\mathfrak{sl}_2)$, where $q$ is a root of unity of odd…

In this paper, we prove the local converse theorem for split even special orthogonal groups over a non-Archimedean local field of characteristic zero. This is the only case left on local converse theorems of split classical groups and the…

Suppose one has a map of split short exact sequences in a category of modules, or more generally, in any abelian category. Do the short exact sequences split compatibly, i.e., does there exist a splitting of each short exact sequence which…