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Pierre R (Jan 29 2025 at 19:54):Hello,
For my research in Applied Category Theory for AI, I will need to understand Monads.
I am a newcomer and my background in CT is Leinster's Basic Category Theory. What would be a good book that introduces Monads?
Thank you
Joe Moeller (Jan 29 2025 at 20:54):What is your mathematical background like? Books like Mac Lane's "Categories for the Working Mathematician" and Riehl's "Category Theory in Context" are aimed at people who know a bit of abstract algebra and topology. For that audience, they're great.
Paolo Perrone (Jan 29 2025 at 21:08):What are you using monads for? Is it probability?
In my work I've often needed monads, mostly to model probability. In the past few years this led me to produce introductory material on monads with this motivation and background in mind. In particular:
I hope this helps!
Pierre R (Jan 30 2025 at 14:15):Joe Moeller said:
What is your mathematical background like? Books like Mac Lane's "Categories for the Working Mathematician" and Riehl's "Category Theory in Context" are aimed at people who know a bit of abstract algebra and topology. For that audience, they're great.
Hello @Joe Moeller, I am a computer scientist. But I am in my second year of a Master's in Mathematics. I think that I have a good algebra background. My topology background is the one needed for analysis, mostly.
Pierre R (Jan 30 2025 at 14:36):Hello @Paolo Perrone
Part of my thesis work is to understand and work through the details of Position: Categorical Deep Learning is an Algebraic Theory of All Architectures. There, the authors use Monads and Algebra of Monads to generalize Geometric Deep Learning.
Additionally, thank you very much for your suggestions. I will try to obtain your book through my university library.
Moreover, I am intrigued by your work. I will take a look at it.
Thank you.
Patrick Nicodemus (Jan 31 2025 at 15:37):@Pierre R Monads can be understood from many different points of view, each of which I think gives a different view. Monads arise in homological algebra, universal algebra and the theory of programming languages, for different reasons.
Pierre R (Jan 31 2025 at 20:16):Patrick Nicodemus said:
Pierre R Monads can be understood from many different points of view, each of which I think gives a different view. Monads arise in homological algebra, universal algebra and the theory of programming languages, for different reasons.
Thank you Patrick for the insight!
Qin Yuxuan (Feb 02 2025 at 09:47):You may be interested in the wiki page Monad (in Computer Science) on nLab.
I think the book Category Theory for Computing Science by Michael Barr and Charles Wells may be helpful as well, particularly Chapter 14 Section 3, "Triple" (another name of monad).
Finally there is a long series about monad on https://stringdiagram.com.
Pierre R (Feb 07 2025 at 20:54):@Qin Yuxuan, thank you! Great resources!