66 citations · 295 across the 23 of their papers we have counts for
27 papers
Extracting Mathematical Concepts from Text
Jacob Collard, Valeria de Paiva, Brendan Fong +1
We investigate different systems for extracting mathematical entities from English texts in the mathematical field of category theory as a first step for constructing a mathematica…
Regular Calculi I: Graphical Regular Logic
Tslil Clingman, Brendan Fong, David I. Spivak
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 repr…
Behavioral Mereology: A Modal Logic for Passing Constraints
Brendan Fong, David Jaz Myers, David I. Spivak
Mereology is the study of parts and the relationships that hold between them. We introduce a behavioral approach to mereology, in which systems and their parts are known only by th…
String Diagrams for Regular Logic (Extended Abstract)
Brendan Fong, David Spivak
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…
Regular and relational categories: Revisiting 'Cartesian bicategories I'
Brendan Fong, David I Spivak
Regular logic is the fragment of first order logic generated by , , , and . A key feature of this logic is that it is the minimal fragment required to exp…
Supplying bells and whistles in symmetric monoidal categories
Brendan Fong, David I Spivak
It is common to encounter symmetric monoidal categories for which every object is equipped with an algebraic structure, in a way that is compatible with the monoidal…
Lenses and Learners
Brendan Fong, Michael Johnson
Lenses are a well-established structure for modelling bidirectional transformations, such as the interactions between a database and a view of it. Lenses may be symmetric or asymme…
Temporal Landscapes: A Graphical Logic of Behavior
Brendan Fong, Alberto Speranzon, David I. Spivak
We present an elementary introduction to a new logic for reasoning about behaviors that occur over time. This logic is based on temporal type theory. The syntax of the logic is sim…
A recipe for black box functors
Brendan Fong, Maru Sarazola
The task of constructing compositional semantics for network-style diagrammatic languages, such as electrical circuits or chemical reaction networks, has been dubbed the black boxi…
Graphical Regular Logic
Brendan Fong, David I Spivak
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…
Behavioral Mereology (Proofs and Properties)
Brendan Fong, David Jaz Myers, David I. Spivak
Mereology is the study of parts and the relationships that hold between them. We introduce a behavioral approach to mereology, in which systems and their parts are known only by th…
Hypergraph Categories
Brendan Fong, David I Spivak
Hypergraph categories have been rediscovered at least five times, under various names, including well-supported compact closed categories, dgs-monoidal categories, and dungeon cate…
Seven Sketches in Compositionality: An Invitation to Applied Category Theory
Brendan Fong, David I Spivak
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…
Backprop as Functor: A compositional perspective on supervised learning
Brendan Fong, David I. Spivak, Rémy Tuyéras
A supervised learning algorithm searches over a set of functions parametrised by a space to find the best approximation to some ideal function . It d…
Universal Constructions for (Co)Relations: categories, monoidal categories, and props
Brendan Fong, Fabio Zanasi
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits an…
Decorated Corelations
Brendan Fong
Let be a category with finite colimits, and let be a factorisation system on with stable under pushouts. Writing $\…
A Universal Construction for (Co)Relations
Brendan Fong, Fabio Zanasi
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits an…
The Algebra of Open and Interconnected Systems
Brendan Fong
Herein we develop category-theoretic tools for understanding network-style diagrammatic languages. The archetypal network-style diagrammatic language is that of electric circuits;…
Corelations are the prop for extraspecial commutative Frobenius monoids
Brandon Coya, Brendan Fong
Just as binary relations between sets may be understood as jointly monic spans, so too may equivalence relations on the disjoint union of sets be understood as jointly epic cospans…
A categorical approach to open and interconnected dynamical systems
Brendan Fong, Paolo Rapisarda, Paweł Sobociński
We develop a sound and complete graphical theory for discrete linear time-invariant dynamical systems. The graphical syntax, as in previous work, is closely related to the classica…
A Compositional Framework for Markov Processes
John C. Baez, Brendan Fong, Blake S. Pollard
We define the concept of an "open" Markov process, or more precisely, continuous-time Markov chain, which is one where probability can flow in or out of certain states called "inpu…
Additive monotones for resource theories of parallel-combinable processes with discarding
Brendan Fong, Hugo Nava-Kopp
A partitioned process theory, as defined by Coecke, Fritz, and Spekkens, is a symmetric monoidal category together with an all-object-including symmetric monoidal subcategory. We t…
A Compositional Framework for Passive Linear Networks
John C. Baez, Brendan Fong
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 describ…
Decorated Cospans
Brendan Fong
Let be a category with finite colimits, writing its coproduct , and let be a braided monoidal category. We describe a method of producing a…