# An Invitation to Applied Category Theory

@inproceedings{Fong2019AnIT, title={An Invitation to Applied Category Theory}, author={Brendan Fong and David I. Spivak}, year={2019} }

Category theory is unmatched in its ability to organize and layer abstractions and to find commonalities between structures of all sorts. No longer the exclusive preserve of pure mathematicians, it is now proving itself to be a powerful tool in science, informatics, and industry. By facilitating communication between communities and building rigorous bridges between disparate worlds, applied category theory has the potential to be a major organizing force. This book offers a self-contained tour…

## 58 Citations

### Notes on Category Theory with examples from basic mathematics

- MathematicsArXiv
- 2019

These notes were originally developed as lecture notes for a category theory course. They should be well-suited to anyone that wants to learn category theory from scratch and has a scientific mind.…

### Diagrammatic sets and rewriting in weak higher categories.

- Mathematics
- 2020

We revisit Kapranov and Voevodsky's idea of spaces modelled on combinatorial pasting diagrams, now as a framework for higher-dimensional rewriting and the basis of a model of weak omega-categories.…

### A Relative Theory of Interleavings

- Mathematics, Computer ScienceArXiv
- 2020

This paper provides a general theory where one maps to a poset that does admit interesting translations, such as the lattice of down sets, and then defines interleavings relative to this map and provides an approximation condition that in the setting of lattices gives rise to two possible pixelizations.

### SKETCHES, QUERIES, VIEWS, AND KLEISLI COMPOSITION: TOWARDS UNIVERSAL ALGEBRA OF DIAGRAMMATIC OPERATIONS WITH PRE- AND POST-CONDITIONS

- Computer Science
- 2020

A very general version of diagram chasing over generalized sketches (in the sense of Makkai) is considered and a project reported in the paper (an accompanying TR can be found online).

### Persistent obstruction theory for a model category of measures with applications to data merging

- Mathematics, Computer ScienceTransactions of the American Mathematical Society, Series B
- 2021

Any collection of databases has a persistence level, which measures the difficulty of JOINing those databases, and this persistent obstruction theory encompasses multi-modal data fusion problems, some forms of Bayesian inference, and probability couplings.

### The algebra and machine representation of statistical models

- Computer ScienceArXiv
- 2020

This dissertation takes steps toward digitizing and systematizing two major artifacts of data science, statistical models and data analyses, by designing and implementing a software system for creating machine representations of data analyses in the form of Python or R programs.

### An Algebra of Resource Sharing Machines

- Mathematics
- 2020

Dynamical systems are a broad class of mathematical tools used to describe the evolution of physical and computational processes. Traditionally these processes model changing entities in a static…

### Open systems in classical mechanics

- MathematicsJournal of Mathematical Physics
- 2021

Author(s): Baez, John C; Weisbart, David; Yassine, Adam | Abstract: Span categories provide a framework for formalizing mathematical models of open systems in classical mechanics. The categories…

### Universal Causality

- MathematicsEntropy
- 2023

Universal Causality is a mathematical framework based on higher-order category theory, which generalizes previous approaches based on directed graphs and regular categories. We present a hierarchical…

### An Enriched Category Theory of Language: From Syntax to Semantics

- Computer ScienceLa Matematica
- 2022

This paper proposes a mathematical framework for passing from probability distributions on extensions of given texts, such as the ones learned by today’s large language models, to an enriched category containing semantic information.