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I read this post on nLab and now I want to learn some order theory. What are good texts that contain the above referenced topics, and are there any that are explicitly about order theory as decategorified category theory (or categorify order theory)? I am especially interested in categorical logic so I especially want to read up on things like Boolean and Heyting algebras, and other relevant topics that I don't yet know about.

Basically I want to use order theory as a stepping stone to learning category theory, and learn some things relevant to logic as I go.

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Just an advice: Learn order theory from books about order theory by order theorists, and learn category theory from books about category theory by category theorists. – Martin Brandenburg May 28 '13 at 21:38
It's not decategorified category theory. It's a special case of category theory. Posets are categories, full stop. – Qiaochu Yuan May 28 '13 at 23:24
More precise: Preorders are those categories in which every diagram commutes. – Martin Brandenburg May 29 '13 at 10:43
So I guess I would be looking for a text on order theory that covers topics that are special cases of important concepts in category theory? Because just looking at the order theory tab on M.SE, there seems to be a lot of ordinals and real analysis questions which I don't think generalize to much interesting stuff in category theory. – fhyve May 30 '13 at 19:03

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