Offtopic: Formalized Gospel theology

This is partly an offtopic post in my math blog. It seems likely that I discovered a category in which such objects as the Father and the Son from the Gospel appear. I am not sure I really discovered God, but this…

Two new chapters in my math draft

I’ve added chapters “Cartesian closedness” and “Singularities” (from the site http://tiddlyspace.com which will be closed soon) to volume 2 draft. Both chapters are very rough draft and present not rigorous proofs but rough ideas.

Directed topological spaces and funcoids

I have researched relations between directed topological spaces and pair of funcoids. Here the first funcoid represents topology and the second one represents direction. Results are mainly negative: Not every directed topological space can be represented as a pair of funcoids. Different…

A new (but easy to prove) theorem in my research book: Theorem Let $latex \mu$ and $latex \nu$ be endomorphisms of some partially ordered dagger precategory and $latex f\in\mathrm{Hom}(\mathrm{Ob}\mu;\mathrm{Ob}\nu)$ be a monovalued, entirely defined morphism. Then $latex f\in\mathrm{C}(\mu;\nu)\Leftrightarrow f\in\mathrm{C}(\mu^{\dagger};\nu^{\dagger}).$

A new math abstraction, categories of sides

I introduce a new math abstraction, categories of sides, in order to generalize two theorems into one. Category of sides $latex \Upsilon$ is an ordered category whose objects are (small) bounded lattices and whose morphisms are maps between lattices such that every…

A new negative result in pointfree topology

I have proved the following negative result: Theorem $latex \mathsf{pFCD} (\mathfrak{A};\mathfrak{A})$ is not boolean if $latex \mathfrak{A}$ is a non-atomic boolean lattice. The theorem is presented in this file. $latex \mathsf{pFCD}(\mathfrak{A};\mathfrak{B})$ denotes the set of pointfree funcoids from a poset $latex \mathfrak{A}$…