This volume provides a systematic presentation of the theory of differential tensor algebras
and their categories of modules. It involves reduction techniques which have proved to be …

This is the fourth part in a series of papers in which we introduce and develop a natural,
general tensor category theory for suitable module categories for a vertex (operator) …

We generalize the definition of an exact sequence of tensor categories due to Bruguières
and Natale, and introduce a new notion of an exact sequence of (finite) tensor categories …

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 …

Indeed , we note that there are algebra i somor p − circlemultiply hisms un derst oo d for alon g
time [B An o the−r motiva Page 1 \noindent 144 \quad Z . L eszcz $ y ˆ{ \acute{n} }$ ski …

Page 1 MEMOIRS Of the American Mathematical Society Number 7Ol On Natural Coalgebra
Decompositions of Tensor Algebras and Loop Suspensions Paul Selick Jie Wu November …

We introduce the notions of normal tensor functor and exact sequence of tensor categories.
We show that exact sequences of tensor categories generalize strictly exact sequences of …

We develop a notion of Morita equivalence for general C-correspondences over C-algebras.
We show that if two correspondences are Morita equivalent, then the tensor algebras built …

We show that, up to Morita equivalence, any standardly stratified algebra, admits an exact
Borel subalgebra. In fact, we show this in the more general case of finite-dimensional …

We introduce (partially) ordered Grothendieck categories and apply results on their structure
to the study of categories of representations of the Mackey Lie algebra of infinite matrices 𝔤 …