Victor Porton's Math Weblog

Significantly updated theory of dependencies (algebraic theory of formulas).

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I have shown that a category (from category theory) can be represented as a pair of a ternary relation and a partial binary operation. This is a possible way of algebraization of category theory. See here.

Note that I use my definition of category with multiple sources and destinations.

Updated my online article Algebraic Theory of Formulas.

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I updated my online article Algebraic Theory of Formulas.

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This short article introduces two modified definitions of category with multiple sources and destinations (from category theory from abstract mathematics).

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I updated my online article Theory of Dependencies (main updates about morphisms between elements and categories of elements, also about composition of dependencies).

Theory of Dependencies is new theory about multidimensional (multi-argument) relations with two special arguments X and Y. This theory is especially important for axiomatic theory of (infinite) mathematical formulas (expressions).

With the idea of categories of elements we can descent from abstractions to concrete things such as categories related with separate elements.

I expect that this theory will supercede both universal algebra and category theory.