Categorification of the Catalan monoid

  title={Categorification of the Catalan monoid},
  author={Anna-Louise Grensing and Volodymyr Mazorchuk},
  journal={Semigroup Forum},
We construct a finitary additive 2-category whose Grothendieck ring is isomorphic to the semigroup algebra of the monoid of order-decreasing and order-preserving transformations of a finite chain. 
Finitary 2-categories associated with dual projection functors
We study finitary 2-categories associated to dual projection functors for finite dimensional associative algebras. In the case of path algebras of admissible tree quivers (which includes all Dynkin
Multisemigroups with multiplicities and complete ordered semi-rings
Motivated by the appearance of multisemigroups in the study of additive 2-categories, we define and investigate the notion of a multisemigroup with multiplicities. This notion seems to be well suited
Diagrams and discrete extensions for finitary 2-representations
  • A. Chan, V. Mazorchuk
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 2017
This paper introduces and investigates the notions of diagrams and discrete extensions in the study of finitary 2-representations of finitarian 2-categories.
Cell structure of bimodules over radical square zero Nakayama algebras
Abstract In this paper, we describe the combinatorics of the cell structure of the tensor category of bimodules over a radical square zero Nakayama algebra. This accounts to an explicit description
Semigroups, multisemigroups and representations
This thesis consists of four papers about the intersection between semigroup theory, category theory and representation theory. We say that a representation of a semigroup by a matrix semigroup is ...
Affine Permutations and an Affine Catalan Monoid
We describe results on pattern avoidance arising from the affine Catalan monoid. The schema of affine codes as canonical decompositions in conjunction with two-row moves is detailed, and then applied
Duflo involutions for 2-categories associated to tree quivers
Motivated by the definition of Duflo involution for fiat $2$-categories, we define certain analogues of Duflo involution for arbitrary finitary $2$-categories and show that such Duflo involutions
Bimodules over uniformly oriented A n quivers with radical square zero
We start with observing that the only connected finite dimensional algebras with finitely many isomorphism classes of indecomposable bimodules are the quotients of the path algebras of uniformly
Representation Theory of Order-Related Monoids of Partial Functions as Locally Trivial Category Algebras
  • Itamar Stein
  • Mathematics
    Algebras and Representation Theory
  • 2019
In this paper we study the representation theory of three monoids of partial functions on an n-set. The monoid of all order-preserving functions (i.e., functions satisfying f(x) ≤ f(y) if x ≤ y) the


Triangulated categories in the representation theory of finite dimensional algebras
Preface 1. Triangulated categories 2. Repetitive algebras 3. Tilting theory 4. Piecewise hereditary algebras 5. Trivial extension algebras References Index.
Additive versus abelian 2-representations of fiat 2-categories
We study connections between additive and abelian 2-rep- resentations of fiat 2-categories, describe combinatorics of 2-categories in terms of multisemigroups and determine the annihilator of a cell
Derived equivalences for symmetric groups and sl2-categorification
We define and study sl2-categorifications on abelian categories. We show in particular that there is a self-derived (even homotopy) equivalence categorifying the adjoint action of the simple
Categorification of the braid groups
We construct a categorification of the braid groups associated with Coxeter groups inside the homotopy category of Soergel's bimodules. Classical actions of braid groups on triangulated categories
Lectures on algebraic categorification
This is a write-up of the lectures given by the author during the Master Class "Categorification" at {\AA}rhus University, Denmark in October 2010.
Methods of Homological Algebra
Considering homological algebra, this text is based on the systematic use of the language and ideas of derived categories and derived functors. Relations with standard cohomology theory are
Cell 2-representations of finitary 2-categories
Abstract We study 2-representations of finitary 2-categories with involution and adjunctions by functors on module categories over finite-dimensional algebras. In particular, we define, construct and
Double Catalan monoids
In this paper, we define and study what we call the double Catalan monoid. This monoid is the image of a natural map from the 0-Hecke monoid to the monoid of binary relations. We show that the double