We classify all fusion categories for a given set of fusion rules with three simple object types.
If a conjecture of Ostrik is true, our classification completes the classification of fusion …

Notions of generalized multicategory have been defined in numerous contexts throughout
the literature, and include such diverse examples as symmetric multicategories, globular …

We give a classification of substructures (= closed subbifunctors) of a given skeletally small
extriangulated category by using the category of defects, in a similar way to the author's …

We form tricategories and the homomorphisms between them into a bicategory, whose 2-
cells are certain degenerate tritransformations. We then enrich this bicategory into an …

We use the string diagram calculus to give graphical proofs of the basic results of Etingof,
Nikshych and Ostrik [On fusion categories, Ann. Math. 162 (2005) 581–642; arXiv …

A bicommutant category is a higher categorical analog of a von Neumann algebra. We study
the bicommutant categories which arise as the commutant C′ of a fully faithful …

We develop the theory of (op) fibrations of 2-multicategories and use it to define abstract six-
functor-formalisms. We also give axioms for Wirthmüller and Grothendieck formalisms …

A notion of mutation of subcategories in a right triangulated category is defined in this article.
When (𝒵, 𝒵) is a 𝒟-mutation pair in a right triangulated category 𝒞, the quotient category 𝒵/𝒟 …

We consider traces on module categories over pivotal fusion categories which are
compatible with the module structure. It is shown that such module traces characterise the …

Extriangulated categories were introduced by Nakaoka and Palu by extracting the
similarities between exact categories and triangulated categories. A notion of mutation of …