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 …

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 …

We characterize discrete (anti-) unitary symmetries and their non-invertible generalizations
in 2+ 1 d topological quantum field theories (TQFTs) through their actions on line operators …

A bstract We develop a mathematical theory of symmetry protected trivial (SPT) orders and
anomaly-free symmetry enriched topological (SET) orders in all dimensions via two different …

Inspired by the study of vertex operator algebra extensions, we answer the question of when
the category of local modules over a commutative exact algebra in a braided finite tensor …

A systematic approach to dualities in symmetric (1+ 1) d quantum lattice models has recently
been proposed in terms of module categories over the symmetry fusion categories. By …

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 …

A bstract In this work, we use Ising chain and Kitaev chain to check the validity of an earlier
proposal in arXiv: 2011.02859 that enriched fusion (higher) categories provide a unified …

We classify various types of graded extensions of a finite braided tensor category BB in
terms of its 2-categorical Picard groups. In particular, we prove that braided extensions of BB …

We study the question of dualizability in higher Morita categories of locally presentable
tensor categories and braided tensor categories. Our main results are that the 3-category of …