The category of finite directed graphs is an excellent thing to think about when considering sketches.
A better way of thinking about categories is as a generalisation of both monoids and preorders.
alti
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When I did my doctorate in computational logic, I got MacLane’s book. It’s not a great first book, but it has some excellent examples, and it’s very much a fore-runner of his collaboration with Moerdijk, “Sheaves in Geometry and Logic”. I learnt more from Lambek and Scott’s book, “Introduction to Higher-Order Categorical Logic”.
The recent article by John Baez is important.
https://johncarlosbaez.wordpress.com/2025/02/08/category-theorists-in-ai/
It outlines applications of category theory to AI safety.
The recent article by John Baez provides motivation:
https://johncarlosbaez.wordpress.com/2025/02/08/category-theorists-in-ai/
It outlines applications of category theory to AI safety.