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I was watching this series of lectures on universal algebra on YouTube and the instructor, Charlotte Aten, mentioned that Øystein Ore studied lattices with the goal of using lattices as a unifying abstraction for mathematical structures. I don't remember which exact lecture she said this in, but she compares the goals of the lattice-based approach with category theory, which has been successful as a unifying abstraction.

I'm curious what the "lattice program" (so to speak) achieved, how it was perceived at the time, where it got stuck, and how it ended.

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I'm the same Charlotte Aten you were watching on YouTube. I had intended to make this a comment and not an answer (since I don't think I can provide a complete one), but since I just joined this StackExchange community for the purpose of responding to this I don't have that ability here yet.

In any case, the main source I have for that story is the book «Modern Algebra and the Rise of Mathematical Structures» by Leo Corry. I don't remember how much depth the author goes into about the short-lived program of Ore's. I think that it was mainly just presented to set the stage for a much more detailed discussion of the history of category theory and as a kind of segue away from abstract/universal algebra. You may be able to find more information in the copious references in that book.

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  • $\begingroup$ I think it is one of the coolest features of Stack Exchange that, sometimes, the person that inspired someone to ask a question comes along an answers it themselves (even if the answer is not complete). $\endgroup$
    – Danu ♦
    Aug 7, 2021 at 16:14

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