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Hoàng Xuân Sính's Thesis: Categorifying Group Theory
John C. Baez
During what Vietnamese call the American War, Alexander Grothendieck spent three weeks teaching mathematics in and near Hanoi. Hoàng Xuân Sính took notes on his lectures and later…
Structured versus Decorated Cospans
John C. Baez, Kenny Courser, Christina Vasilakopoulou
One goal of applied category theory is to understand open systems. We compare two ways of describing open systems as cospans equipped with extra data. First, given a functor $L \co…
Categories of Nets
John C. Baez, Fabrizio Genovese, Jade Master +1
We present a unified framework for Petri nets and various variants, such as pre-nets and Kock's whole-grain Petri nets. Our framework is based on a less well-studied notion that we…
Structured Cospans
John C. Baez, Kenny Courser
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…
Enriched Lawvere Theories for Operational Semantics
John C. Baez, Christian Williams
Enriched Lawvere theories are a generalization of Lawvere theories that allow us to describe the operational semantics of formal systems. For example, a graph enriched Lawvere theo…
Network Models from Petri Nets with Catalysts
John C. Baez, John Foley, Joe Moeller
Petri networks and network models are two frameworks for the compositional design of systems of interacting entities. Here we show how to combine them using the concept of a "catal…
Open Petri Nets
John C. Baez, Jade Master
The reachability semantics for Petri nets can be studied using open Petri nets. For us an "open" Petri net is one with certain places designated as inputs and outputs via a cospan…
Props in Network Theory
John C. Baez, Brandon Coya, Franciscus Rebro
Long before the invention of Feynman diagrams, engineers were using similar diagrams to reason about electrical circuits and more general networks containing mechanical, hydraulic,…
Operads and Phylogenetic Trees
John C. Baez, Nina Otter
We construct an operad whose operations are the edge-labelled trees used in phylogenetics. This operad is the coproduct of , the operad for commutativ…
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…
Categories in Control
John C. Baez, Jason Erbele
Control theory uses "signal-flow diagrams" to describe processes where real-valued functions of time are added, multiplied by scalars, differentiated and integrated, duplicated and…
Lectures on n-Categories and Cohomology
John C. Baez, Michael Shulman
The goal of these talks was to explain how cohomology and other tools of algebraic topology are seen through the lens of n-category theory. Special topics include nonabelian cohomo…