Category theory is unmatched in its ability to organize and layer abstractions and to find
commonalities between structures of all sorts. No longer the exclusive preserve of pure …

This book is an invitation to discover advanced topics in category theory through concrete,
real-world examples. It aims to give a tour: a gentle, quick introduction to guide later …

Cyber-physical systems require the construction and management of various models to
assure their correct, safe, and secure operation. These various models are necessary …

Lenses have a rich history and have recently received a great deal of attention from applied
category theorists. We generalize the notion of lens by defining a category $\mathsf {Lens} …

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 …

Dynamical systems are ubiquitous in science and engineering as models of phenomena
that evolve over time. Although complex dynamical systems tend to have important modular …

We lift the standard equivalence between fibrations and indexed categories to an
equivalence between monoidal fibrations and monoidal indexed categories, namely weak …

We introduce the normal produoidal category of monoidal contexts over an arbitrary
monoidal category. In the same sense that a monoidal morphism represents a process, a …

i September 3, 2023 Page 1 i DRAFT September 3, 2023 Page 2 Categorical Systems
Theory David Jaz Myers (Last updated: September 3, 2023) Page 3 iii This page …

Structured Versus Decorated Cospans Page 1 Volume 4 Issue 3 ISSN 2631-4444 Structured
Versus Decorated Cospans John C. Baez1,2, Kenny Courser1, and Christina Vasilakopoulou3 …