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December 31, 2010 / porton

Pointfree funcoids – a category

I updated the draft of my article “Pointfree Funcoids” at my Algebraic General Topology site. The new version of the article defines pointfree funcoids differently than before: Now a pointfree funcoid may have different posets as its source and destination. So pointfree funcoids now form a category whose objects are posets with least element and whose morphisms are pointfree funcoids.

This version of the article is yet a preliminary draft.

Pointfree funcoids is a rather routine and boring generalization of funcoids. This is unlike locales and frames which are not an obvious generalization of topological spaces. My routine work about pointfree funcoids will continue in adding maybe some more generalizations of theorems about funcoids and checking my drafts for errors. Afterward I will switch using the theory of pointfree funcoids to more interesting and fascinating work about n-ary funcoids, products of funcoids, compact funcoid, etc.

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