I’ve published a new edition of my book Algebraic General Topology. The new edition features “unfixed morphisms” a way to turn a category into a semigroup. (Certain additional structure on the category is needed.) The book features a wide generalization of general…
read moreI have rewritten the section “More results on restricted identities” of this draft. Now it contains some new (easy but important) formulas.
read moreI 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…
read moreI 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.
read moreI 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…
read moreIn 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…
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Algebraic general topology Category theory Filters General Topology Math on the Web Open problems Pointfree topology Publications
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…
read moreI’ve added to my book a theorem with a triangular diagram of isomorphisms about representing filters on a set as unfixed filters or as filters on the poset of all small (belonging to a Grothendieck universe) sets. The theorem is in the…
read moreI proved: Theorem $latex T$ is a left adjoint of both $latex F_{\star}$ and $latex F^{\star}$, with bijection which preserves the “function” part of the morphism. The details and the proof is available in the draft of second volume of my online book. The…
read moreI started research of mappings between endofuncoids and topological spaces. Currently the draft is located in volume 2 draft of my online book. I define mappings back and forth between endofuncoids and topologies. The main result is a representation of an endofuncoid…
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