Author: Victor Porton

I am Victor Porton, the mathematician who discovered ordered semigroup actions. Among with that ordered semicategory actions stuff, I discovered SEVERAL mathematical theories that are as much general and fruitful as group theory. That I discovered several such things makes me the best mathematician (the smartest person in known History), because AFAIK nobody else discovered more than one such thing. I also won several blockchain hackathons. So, I am a highly skilled blockchain programmer. I am also highly skilled in such technologies as XML, PostgreSQL, Linux, Rust, D. I am the main owner of this business, chief editor of this blog, and creator of this site.

New concept in category theory: “unfixed morphisms”

I have developed my little addition to category theory, definition and research of properties of unfixed morphisms. Unfixed morphisms is a tool for turning a category (with certain extra structure) into a semigroup, that is abstracting away objects. Currently this research is available in this draft. I am going to rewrite my online book using […]

Removed some sections from my draft

I removed from my draft sections about “categories under Rel”. The removal happened because I developed a more general and more beautiful theory. The old version is preserved in Git history.

Restricted identity axioms changed

I announced that I have introduces axioms for “restricted identities”, a structure on a category which allows to turn the category into a semigroup (abstracting away objects). But I noticed that these axioms do not fit into concrete examples which I am going to research. So I have rewritten the text about restricted identities with […]

“Unfixed filters” rewritten

“Unfixed filter” section of my book was rewritten for more general lattices instead of old version with a certain lattice of sets.

Categories with restricted identities

In this draft (to be moved into the online book in the future, but the draft is nearing finishing this topic, not including functors between categories with restricted identities) I described axioms and properties of categories with restricted identities. Basically, a category with restricted identities is a category $latex \mathcal{C}$ together with morphisms $latex \mathrm{id}^{\mathcal{C}(A,B)}_X$ […]

“Unfixed filters” research now in the book volume-1

I essentially finished my research of unfixed filters. I moved all research of unfixed filters to volume-1.pdf. Particularly now it contains subsections “The lattice of unfixed filters” and “Principal unfixed filters and filtrator of unfixed filters”. Now I am going to research unfixed reloids and unfixed funcoids (yet to be defined).

I strengthened a theorem

I strengthened a theorem: It is easily provable that every atomistic poset is strongly separable (see my book). It is a trivial result but I had a weaker theorem in my book before today.

Math volunteer job

I welcome you to the following math research volunteer job: Participate in writing my math research book (volumes 1 and 2), a groundbreaking general topology research published in the form of a freely downloadable book: implement existing ideas, propose new ideas develop new theories solve open problems write and rewrite the book and other files […]