I’ve fixed the error in my proof
I have quickly corrected the error in my proof of an important theorem. Now it is even more beautiful.
Error in my proof
That proof which I claimed in this blog post is with an error: I have messed product of objects and product of morphisms. Now I desperately attempt to repair the proof.
Direct product in the category of continuous maps between endofuncoids
I released a rough draft of my article Direct product in the category of continuous maps between endofuncoids. This (among other) solves the problem I proposed in this blog post. Previously I have said that my research got stuck. Now I see how to continue it! I am again blessed.
The (candidate) construction of direct product in the category of continuous maps between endo-funcoids
Consider the category of (proximally) continuous maps (entirely defined monovalued functions) between endo-funcoids. Remind from my book that morphisms $latex f: A\rightarrow B$ of this category are defined by the formula $latex f\circ A\sqsubseteq B\circ f$ (here and below by abuse of notation I equate functions with corresponding principal funcoids). Let $latex F_0, F_1$ are […]
Subatomic products – a new kind of product of funcoids
I’ve discovered a new kind of product of funcoids, which I call subatomic product. Definition Let $latex f : A_0 \rightarrow A_1$ and $latex g : B_0 \rightarrow B_1$ are funcoids. Then $latex f \times^{\left( A \right)} g$ (subatomic product) is a funcoid $latex A_0 \times B_0 \rightarrow A_1 \times B_1$ such that for every […]
A conjecture about direct product of funcoids
I am attempting to define direct products in the category cont(mepfFcd) (the category of monovalued, entirely defined continuous pointfree funcoids), see this draft article for a definition of this category. A direct product of objects may possibly be defined as the cross-composition product (see this article). A candidate for product of morphisms $latex f_1:\mathfrak{A}\rightarrow\mathfrak{B}$ and […]
“Categories related with funcoids”, a new draft
I started to write a new article Categories related with funcoids. It is now a very preliminary partial draft.