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

Diagrams and discrete extensions for finitary 2-representations

  • A. ChanV. 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.

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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

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  • 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


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17 Quivers of Monoid Algebras

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Simple transitive $2$-representations of small quotients of Soergel bimodules

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