This article is intended as a reference guide to various notions of monoidal categories and
their associated string diagrams. It is hoped that this will be useful not just to …

We present a novel approach for recognizing faces in images taken from different directions
and under different illumination. The method is based on a 3D morphable face model that …

There are many situations in logic, theoretical computer science, and category theory where
two binary operations—one thought of as a (tensor)“product”, the other a “sum”—play a key …

This paper revisits the authors' notion of a differential category from a different perspective. A
differential category is an additive symmetric monoidal category with a comonad (a …

Following work of Ehrhard and Regnier, we introduce the notion of a differential category: an
additive symmetric monoidal category with a comonad (a 'coalgebra modality') and a …

String diagrams turn algebraic equations into topological moves that have recurring shapes,
involving the sliding of one diagram past another. We individuate, at the root of this fact, the …

Substructural logics are traditionally obtained by dropping some or all of the structural rules
from Gentzen's sequent calculi LK or LJ. It is well known that the usual logical connectives …

We introduce monoidal streams: a generalization of causal stream functions to monoidal
categories. In the same way that streams provide semantics to dataflow programming with …

We universally characterize the produoidal category of monoidal lenses over a monoidal
category. In the same way that each category induces a cofree promonoidal category of …

String diagrams were introduced by Roger Penrose as a handy notation to manipulate
morphisms in a monoidal category. In principle, this graphical notation should encompass …