7 papers
Diagrammatics for lax and Frobenius monoidal functors and weak morphism classifiers
Alexis Langlois-Rémillard, Mateusz Stroiński
The theory of 2-monads entails that, for a strict monoidal category C, there is a strict monoidal category L(C) such that strict monoidal functors from L(C) are precisely the lax m…
Finite Pre-Tensor Categories that are Morita Equivalent to Finite Tensor Categories
Thibault D. Décoppet, Mateusz Stroiński
A finite pre-tensor category is a finite abelian category equipped with a right exact tensor product for which every projective object has duals. Finite tensor categories, for whic…
Algebras in fusion categories: species and hereditary algebras
Edmund Heng, Mateusz Stroiński
We initiate the study of non-semisimple algebras in fusion categories by establishing the framework of -species -- analogous to the framework of species and quivers us…
Hochschild cohomology for finitary 2-representations
James Macpherson, Vanessa Miemietz, Mateusz Stroiński
In this article, we define and investigate Hochschild cohomology for finitary 2-representations of quasi-fiat 2-categories.
A Coboundary Temperely-Lieb Category for -Crystals
Moaaz Alqady, Mateusz Stroiński
By considering a suitable renormalization of the Temperley--Lieb category, we study its specialization to the case . Unlike the case, the obtained monoidal category,…
Simple algebras and exact module categories
Kevin Coulembier, Mateusz Stroiński, Tony Zorman
We verify a conjecture of Etingof and Ostrik, stating that an algebra object in a finite tensor category is exact if and only if it is a finite direct product of simple algebras. T…
Reconstruction of module categories in the infinite and non-rigid settings
Mateusz Stroiński, Tony Zorman
By building on the notions of internal projective and injective objects in a module category introduced by Douglas, Schommer-Pries, and Snyder, we extend the reconstruction theory…