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 …

A bstract Gauging is a powerful operation on symmetries in quantum field theory (QFT), as it
connects distinct theories and also reveals hidden structures in a given theory. We initiate a …

We apply the yoga of classical homotopy theory to classification problems of G-extensions of
fusion and braided fusion categories, where G is a finite group. Namely, we reduce such …

A bstract We consider the triality fusion category discovered in the c= 1 Kosterlitz-Thouless
theory [1]. We analyze this fusion category using the tools from the group theoretical fusion …

We introduce two new classes of fusion categories which are obtained by a certain
procedure from finite groups–weakly group-theoretical categories and solvable categories …

Although it has been a well-known fact, for more than two decades, that category theory is
needed for the study of topological orders, it is still a non-trivial challenge for students and …

In this paper, we study the twisted gauging on the (1+ 1) d lattice and construct various non-
local mappings on the lattice operators. To be specific, we define the twisted Gauss law …

The balanced tensor product M⊗ AN of two modules over an algebra A is the vector space
corepresenting A-balanced bilinear maps out of the product M× N. The balanced tensor …

We introduce a finiteness property for braided fusion categories, describe a conjecture that
would characterize categories possessing this, and verify the conjecture in a number of …

FUSION 2-CATEGORIES WITH NO LINE OPERATORS ARE GROUPLIKE Page 1 Bull. Aust.
Math. Soc. 104 (2021), 434–442 doi:10.1017/S0004972721000095 FUSION 2-CATEGORIES …