66 citations · 295 across the 23 of their papers we have counts for
13 papers · 1 filter
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…
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…
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…
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…
Decorated Corelations
Brendan Fong
Let be a category with finite colimits, and let be a factorisation system on with stable under pushouts. Writing $\…
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 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…