172 citations · 796 across the 66 of their papers we have counts for
7 papers · 1 filter
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…
Evaluating the Pixel Array Method as Applied to Partial Differential Equations
Cynthia T. Liu, David I. Spivak
The Pixel Array (PA) Method, originally introduced by Spivak et. al., is a fast method for solving nonlinear or linear systems. One of its distinguishing features is that it presen…
Decomposition-space slices are toposes
Joachim Kock, David I. Spivak
We show that the category of decomposition spaces and CULF maps is locally a topos. Precisely, the slice category over any decomposition space D is a presheaf topos, namely decomp/…
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…