# Notes on Category Theory with examples from basic mathematics

@article{Perrone2019NotesOC, title={Notes on Category Theory with examples from basic mathematics}, author={Paolo Perrone}, journal={ArXiv}, year={2019}, volume={abs/1912.10642} }

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. There is no need to know advanced mathematics, nor any of the disciplines where category theory is traditionally applied, such as algebraic geometry or theoretical computer science. The only knowledge that is assumed from the reader is linear algebra. All concepts are explained by giving concrete…

## 6 Citations

On my favorite conventions for drawing the missing diagrams in Category Theory

- Art
- 2020

I used to believe that my conventions for drawing diagrams for categorical statements could be written down in one page or less, and that the only tricky part was the technique for reconstructing…

Representable Markov Categories and Comparison of Statistical Experiments in Categorical Probability

- MathematicsArXiv
- 2020

This work states and proves equivalent conditions for second-order stochastic dominance and lays foundation for the theory of comparing statistical experiments within Markov categories by stating and proving the classical Blackwell-Sherman-Stein Theorem.

CertRL: formalizing convergence proofs for value and policy iteration in Coq

- Computer ScienceCPP
- 2021

A Coq formalization of two canonical reinforcement learning algorithms: value and policy iteration for finite state Markov decision processes and a contraction property of Bellman optimality operator to establish that a sequence converges in the infinite horizon limit.

Category theory with examples in probability theory

- Mathematics
- 2021

1 1 Category Theory 2 1.1 Categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Funtor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3…

Nets with Mana: A Framework for Chemical Reaction Modelling

- Computer ScienceICGT
- 2021

We use categorical methods to define a new flavor of Petri nets which could be useful in modelling chemical reactions.

The Category Theory of Causal Models

- Mathematics, Philosophy
- 2020

Building on work of Rubenstein et al, we consider a notion of structurepreserving transformations between structural causal models. We describe a category, in the sense of category theory, of such…

## References

SHOWING 1-10 OF 16 REFERENCES

Categorical Homotopy Theory

- Mathematics
- 2014

This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters…

An Invitation to Applied Category Theory

- Mathematics
- 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…

A Survey of Graphical Languages for Monoidal Categories

- Mathematics
- 2010

This article is intended as a reference guide to various notions of monoidal categories and their associated string diagrams. It is hoped that this will be useful not just to mathematicians, but also…

Category Theory Using String Diagrams

- Computer ScienceArXiv
- 2014

This work develops string diagrammatic formulations of many common notions, including adjunctions, monads, Kan extensions, limits and colimits, and describes representable functors graphically, and exploits these as a uniform source of graphical calculation rules for many category theoretic concepts.

Set theory for category theory

- Mathematics, Philosophy
- 2008

Questions of set-theoretic size play an essential role in category theory, especially the distinction between sets and proper classes (or small sets and large sets). There are many different ways to…

Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning

- Physics
- 2017

This entirely diagrammatic presentation of quantum theory represents the culmination of ten years of research, uniting classical techniques in linear algebra and Hilbert spaces with cutting-edge developments in quantum computation and foundations.

A LEISURELY INTRODUCTION TO SIMPLICIAL SETS

- Mathematics
- 2011

Simplicial sets are introduced in a way that should be pleasing to the formally-inclined. Care is taken to provide both the geometric intuition and the categorical details, laying a solid foundation…

Seven Sketches in Compositionality: An Invitation to Applied Category Theory

- Mathematics
- 2018

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 exploration. The…

Abstract and Concrete Categories - The Joy of Cats

- Mathematics
- 1990

This chapter discusses Categories and Functors, Topological Categories, Partial Morphisms, Quasitopoi, and Topological Universes, as well as partial Morphisms in Abstract Categories and Cartesian Closed Categories.