The way below relation is used to define compact elements in a dcpo. Can someone explain compactness and an object way below itself. Also, when we abstract this relation to categories, where the order structure is represented by morphisms, please explain compactness in this sense too.
2026-04-05 23:42:57.1775432577
Explain the compactness relation for elements of dcpos and also in a category if objects
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I believe that the nlab answers this really well.
compact element in dcpo https://ncatlab.org/nlab/show/compact+element
compact object in category theory https://ncatlab.org/nlab/show/compact+object