## 24 Citations

Supplying bells and whistles in symmetric monoidal categories.

- Mathematics
- 2019

It is common to encounter symmetric monoidal categories $\mathcal{C}$ for which every object is equipped with an algebraic structure, in a way that is compatible with the monoidal product and unit in…

Structured Cospans

- Mathematics
- 2019

One goal of applied category theory is to better understand networks appearing throughout science and engineering. Here we introduce "structured cospans" as a way to study networks with inputs and…

Regular and relational categories: Revisiting 'Cartesian bicategories I'

- Philosophy, Mathematics
- 2019

Regular logic is the fragment of first order logic generated by $=$, $\top$, $\wedge$, and $\exists$. A key feature of this logic is that it is the minimal fragment required to express composition of…

Monoidal Grothendieck Construction

- Mathematics
- 2018

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

String Diagrams for Regular Logic (Extended Abstract)

- MathematicsACT
- 2019

The syntax and proof rules of regular logic are understood in terms of the free regular category FRg(T) on a set T to show that every natural category has an associated regular calculus, and conversely from every regular calculus one can construct a regular category.

C T ] 2 0 Ju n 20 19 Graphical Regular Logic

- Mathematics, Philosophy
- 2019

Regular logic can be regarded as the internal language of regular categories, but the logic itself is generally not given a categorical treatment. In this paper, we understand the syntax and proof…

String Diagram Rewrite Theory I: Rewriting with Frobenius Structure

- Computer ScienceJ. ACM
- 2022

This work introduces a combinatorial interpretation of string diagram rewriting modulo Frobenius structures in terms of double-pushout hypergraph rewriting, and proves this interpretation to be sound and complete and shows that the approach can be generalised to rewrite modulo multiple Frobenii structures.

Bialgebraic foundations for the operational semantics of string diagrams

- Computer ScienceInf. Comput.
- 2021

Wiring diagrams as normal forms for computing in symmetric monoidal categories

- Computer ScienceACT
- 2020

An "unbiased" approach to implementing symmetric monoidal categories, based on an operad of directed, acyclic wiring diagrams, is presented, because the interchange law and other laws of a SMC hold identically in a wiring diagram.

Regular Calculi I: Graphical Regular Logic

- Mathematics
- 2021

What is ergonomic syntax for relations? In this first paper in a series of two, to answer the question we define regular calculi: a suitably structured functor from a category representing the syntax…

## References

SHOWING 1-10 OF 24 REFERENCES

Decorated Cospans

- Mathematics
- 2015

Let C be a category with finite colimits, writing its coproduct +, and let (D,⊗) be a braided monoidal category. We describe a method of producing a symmetric monoidal category from a lax braided…

The operad of wiring diagrams: formalizing a graphical language for databases, recursion, and plug-and-play circuits

- Computer ScienceArXiv
- 2013

It is shown that wiring diagrams form the morphisms of an operad $\mcT$, capturing this self-similarity, and is moved on to show how plug-and-play devices and also recursion can be formulated in the operadic framework as well.

Algebras of Open Dynamical Systems on the Operad of Wiring Diagrams

- Mathematics, Computer Science
- 2014

This paper uses the language of operads to study the algebraic nature of assembling complex dynamical systems from an interconnection of simpler ones, and defines two W-algebras, G and L, which associate semantic content to the structures in W.

Mathematics

- MathematicsNature
- 1935

AbstractTHE calculus of matrices has had a curious history. It was first used by Hamilton in 1853 under the name of “Linear and Vector Functions”. Cay ley used the term matrix in 1854, and developed…

GENERIC COMMUTATIVE SEPARABLE ALGEBRAS AND COSPANS OF GRAPHS

- Mathematics, Computer Science
- 2005

We show that the generic symmetric monoidal category with a commu- tative separable algebra which has a Σ-family of actions is the category of cospans of finite Σ-labelled graphs restricted to finite…

A compositional framework for Markov processes

- Mathematics, Computer Science
- 2016

It is proved that black boxing gives a symmetric monoidal dagger functor sending open detailed balanced Markov processes to open circuits made of linear resistors, and described how to “black box” an open Markov process.

A Compositional Framework for Passive Linear Networks

- Mathematics
- 2015

Passive linear networks are used in a wide variety of engineering applications, but the best studied are electrical circuits made of resistors, inductors and capacitors. We describe a category where…

The operad of temporal wiring diagrams: formalizing a graphical language for discrete-time processes

- Computer ScienceArXiv
- 2013

This work investigates the hierarchical structure of processes using the mathematical theory of operads, and defines an operad of black boxes and directed wiring diagrams of processes (which it is called propagators, after Radul and Sussman), which are useful for modeling dynamic flows of information.