Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio
is not an integer! But this can happen for generalizations of vector spaces—objects of a …

Using a variety of methods developed in the literature (in particular, the theory of weak Hopf
algebras), we prove a number of general results about fusion categories in characteristic …

Working over an arbitrary field, we define compact semisimple 2-categories, and show that
every compact semisimple 2-category is equivalent to the 2-category of separable module 1 …

Almost since the advent of skein-theoretic invariants of knots and links (the Jones, HOMFLY,
and Kauffman polynomials), the important role of categories of tangles in the connection …

We generalize Rost's theory of cycle modules [20] using the Milnor-Witt K-theory instead of
the classical Milnor K-theory. We obtain a (quadratic) setting to study general cycle …

We study the cohomology theory and the canonical Milnor-Witt cycle module associated to a
motivic spectrum. We prove that the heart of Morel-Voevodsky stable homotopy category …

We combine the theory of inductive data types with the theory of universal measurings. By
doing so, we find that many categories of algebras of endofunctors are actually enriched in …

We show that the Gerstenhaber-Schack cohomology of a Hopf algebra determines its
Hochschild cohomology, and in particular its Gerstenhaber-Schack cohomological …

Davydov-Yetter cohomology classifies infinitesimal deformations of tensor categories and of
tensor functors. Our first result is that Davydov-Yetter cohomology for finite tensor categories …

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 …