Related papers: Cancellative conjugation semigroups and monoids
We study simple and projective modules of a certain class of Ehresmann semigroups, a well-studied generalization of inverse semigroups. Let $S$ be a finite right (left) restriction Ehresmann semigroup whose corresponding Ehresmann category…
The themes of cancellation, internal cancellation, substitution have led to a lot of interesting research in the theory of modules over commutative and noncommutative rings. In this paper, we introduce and study cancellation problem in the…
In this note we give two examples of partially commutative subgroups of partially commutative groups. Our examples are counterexamples to the Extension Graph Conjecture and to the Weakly Chordal Conjecture of Kim and Koberda, \cite{KK}. On…
A super-modular category is a unitary pre-modular category with M\"uger center equivalent to the symmetric unitary category of super-vector spaces. Super-modular categories are important alternatives to modular categories as any unitary…
The Schur orthogonality relations are a cornerstone in the representation theory of groups. We utilize a generalization to weak Hopf algebras to provide a new, readily verifiable condition on the skeletal data for deciding whether a given…
We characterize projective objects in the category of internal crossed modules within any semi-abelian category. When this category forms a variety of algebras, the internal crossed modules again constitute a semi-abelian variety, ensuring…
We study the path category of an inverse semigroup admitting unique maximal idempotents and give an abstract characterization of the inverse semigroups arising from zigzag maps on a left cancellative category. As applications we show that…
We characterize the inverse semigroups that are Morita equivalent to graph inverse semigroups. We also consider a generalization to inverse semigroups associated with left cancellative categories.
In this paper we introduce the category of strong Hopf modules for a weak Hopf quasigroup H in a braided monoidal category. We also prove that this category is equivalent to the category of right modules over the image of the target…
Let $A$ be a separable simple exact ${\cal Z}$-stable $C^*$-algebra. We show that the unitay group of ${\tilde A}$ has the cancellation property. If $A$ has continuous scale, the Cuntz semigroup of $\tilde A$ has the strict comparison…
A semisimple algebraic tensor category over an algebraically closed field k of characteristic zero is the representation category of all finite dimensional twisted super representations of an affine reductive supergroup G over k. Such a…
Following Krause \cite{Kr}, we prove Krull-Schmidt type decomposition theorems for thick subcategories of various triangulated categories including the derived categories of rings, Noetherian stable homotopy categories, stable module…
An elementary proof is given for the fact that every locally compact subsemigroup of a compact topological group is a closed subgroup. A sample consequence is that every commutative cancellative pseudocompact locally compact Hausdorff…
We study the arithmetic of seminormal $v$-noetherian weakly Krull monoids with nontrivial conductor which have finite class group and prime divisors in all classes. These monoids include seminormal orders in holomorphy rings in global…
We show that abstract Cuntz semigroups form a closed symmetric monoidal category. Thus, given Cuntz semigroups $S$ and $T$, there is another Cuntz semigroup $[[S,T]]$ playing the role of morphisms from $S$ to $T$. Applied to C$^*$-algebras…
Let $G$ be a simple algebraic group of exceptional type over an algebraically closed field of characteristic $p > 0$. This paper continues a long-standing effort to classify the connected reductive subgroups of $G$. Having previously…
We study actions of (infinitely presented) graphical small cancellation groups on the Gromov boundaries of their coned-off Cayley graphs. We show that a class of graphical small cancellation groups, including (infinitely presented)…
A full subcategory of modules over a commutative ring $R$ is wide if it is abelian and closed under extensions. Hovey \cite{wide} gave a classification of wide subcategories of finitely presented modules over regular coherent rings in terms…
Idempotent states on locally compact quantum semigroups with weak cancellation properties are shown to be Haar states on a certain sub-object described by an operator system with comultiplication. We also give a characterization of the…
Weakly Schreier split extensions are a reasonably large, yet well-understood class of monoid extensions, which generalise some aspects of split extensions of groups. This short note provides a way to define and study similar classes of…