Category without the requirement of Hom-sets to be disjoint
From this Math.SE post: It would be helpful to have a standard term XXX for “a category without the requirement of Hom-sets to be disjoint” and “category got from XXX by adding source and destination object to every morphism”. This would greatly help to simplify at least 50% of routine definitions of particular categories. Why […]
The article about ordinal numbers and product
I’ve sent this article to an open access peer reviewed journal: A New Kind of Product of Ordinal Number of Relations having Ordinal Numbers of Arguments (the article is available online).
An article about functions taking ordinal number of arguments
I’ve put online this article. It is a rough draft, is incomplete and contains little errors. Nevertheless I hope you’ll enjoy reading it: A New Kind of Product of Ordinal Number of Relations having Ordinal Numbers of Arguments
Circuitoids, a Generalization of Categories
Circuitoids are a generalization of a category where each morphisms has an arbitrary (possibly infinite) number of arguments. Two morphisms are not required to have the same number of arguments. See this manuscript where I first define circuitoids. I haven’t (yet) defined some notion of associativity for circuitoids. This may be a topic of our […]
A proposal for arXiv – managing patches
A famous mathematician Gowers wrote that it is needed “a positive strategy of actually setting up a new system might work rather better” for publishing math articles. In this post I suggest a way for the community to improve quality of self-published (or self-archived as scientists say) articles. I suggest to add the following feature […]
I am changing my research field
I failed to make progress in research of product of funcoids, the next thing I should research in my research plan. I also fail to solve any of my open problems. Thus my research is stalled. I hope other people can solve the problems I formulated. Due this crisis I decide to change my research […]
Untyped formalized systems are wrong
First, I’m not (yet) an expert in formalized mathematics. I know Isabelle/ZF better, but have only overall view of Isabelle/HOL. Nevertheless I want to tell my opinion on typed (such as HOL) vs. untyped (such as Isabelle/ZF) systems. Slawomir Kolodynski converted me into his religion of doing formalized math with Isabelle/ZF and answering “yes” to […]
My motivation to do math research
In the past I considered my purpose to exactly and directly follow commandments of Bible. I had some purposes hardly set as the aim of my life. My life was driven by these purposes not by my wish or my heart. I understood that it was wrong, Bible is more subtle than just a list […]
Restricting a reloid to a trivial atomic filter object
I proved the following (not very hard) theorem: Theorem $latex f|^{\mathsf{RLD}}_{\{ \alpha \}} = \{ \alpha \} \times^{\mathsf{RLD}} \mathrm{im} \left( f|^{\mathsf{RLD}}_{\{ \alpha \}} \right)$ for every reloid $latex f$ and $latex \alpha \in \mho$. See the online article about funcoids and reloids.
My math sickness
I’m sick with the following: I repeatedly formulate conjectures which have trivial counterexamples and am stuck attempting to prove these true not seeing counterexamples. I should less rely on my ideas what is a true conjecture. I just need to become humbler and less proud. Hopefully now I have enough counter-examples for me to follow […]