Victor Porton's Math Weblog

Conjecture about binary relations:

Let f and g are binary relations, g is a subset of f. If gg^-1 = fg^-1, then exists a set K such that g = f|_K.

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I suggest to add Category of Endomorphisms to program of math and computer science faculties of Universities. It should be added as a sub-course of Category theory university course.

This is especially important for Math Logic and Computer Science students, and also important for algebraists.

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Category of Endomorphisms and Pseudomorphisms online article updated.

The article is about categories whose objects are endomorphisms of any given category. Particularly is considered the case of a category with partially ordered morphisms. It produces a rich, interesting theory.

The section Category of Elements and below is completely reworked. (There were serious errors, now they are corrected.)

Category of epimorphisms and pseudomorphims (online article) updated with several new theorems, corrections of mistakes, and some new concepts.

This article considers an interesting category whose objects are endomorphisms of an arbitrary category with possibly partially ordered morphisms.

It is used for my algebraic theory of formulas. It will be also used in other fields of mathematics.

Online article (yet partial) about morphisms (I call these pseudomorphisms) of endomorphisms of a category with partially ordered morphisms (my new theory).

Pseudomorphism f from an endomorphism U to an endomorphism V is defined by formula f U \subseteq V f.

This is a purely categorical generalization of some aspects of my theory of dependencies, the theory of multidimensional relations (considered as generalization of binary relations) with special parameters X and Y. This theory is important for algebraic theory of formulas (expressions).

Read article online: Category of Endomorphisms and Pseudomorphisms.