Wiki to prove that certain categories are cartesian closed
I have announced that I have proved that Category of continuous maps between endofuncoids is cartesian closed. This was a fake alarm, my proof was with a crucial error. Now I have put the problem and some ideas how to prove it in a wiki. So I announce a new project akin to Polymath Project. […]
Category of continuous maps between endofuncoids is cartesian closed
I rough draft article I prove that the category of continuous maps between endofuncoids is cartesian closed. Whether the category of continuous maps between endoreloids is cartesian closed, is yet an open problem.
Changes to my article about products in certain categories
There are two changes in Products in dagger categories with complete ordered Mor-sets draft article: 1. I’ve removed the section on relation of subatomic product with categorical product saying that for funcoids they are the same. No, they are not the same. My claim that they are the same was false. 2. Added section “Special […]
A suggested way to solve an open problem
On the task formulated in this blog post: An attempt to prove that $latex \mathrm{GR} ( \Delta \times^{\mathsf{FCD}} \Delta)$ is closed under finite intersections (see http://portonmath.tiddlyspace.com/#[[Singularities%20funcoids%3A%20some%20special%20cases]]) http://portonmath.tiddlyspace.com/#[[Singularities%20funcoids%3A%20special%20cases%20proof%20attempts]]
A wiki about applying generalized limit to singularities theory
I have created a wiki about development of theory of singularities using generalized limits. Please read my book (where among other I define generalized limits) and then participate in this research wiki. Study singularities in this novel approach and share Nobel Prize with me!
My gibberish with partial proofs
I’ve put online my gibberish with partial proofs and proof attempts of my open problems. You can see the PDF file with this gibberish. Please write me (either by email or by blog comments) if you solve anything of this.
A few new conjectures
Conjecture 1. The categories Fcd and Rld are complete and co-complete (actually 4 conjectures). I have not yet spend much time trying to solve this conjecture, it may be probably easy. Conjecture 2. The categories Fcd and Rld are cartesian closed (actually two conjectures).
New chapter in my book
I have added new chapter: 9 “On distributivity of composition with a principal reloid” into my research monograph preprint. (Read the book) The chapter is centered over a single theorem that composition with a principal reloid is distributive over join of reloids. It also defines an embedding from the set of reloids to the set […]
Embedding reloids into funcoids
I have codified my idea how to embed reloids into funcoids in this draft article. Next I am going to attempt to solve some of my conjectures using this embedding. I will announce in this blog how solving the open problems goes. For the moment, I have also noticed a new problem: Conjecture $latex \rho […]
Decomposition of composition and a partial proof of a conjecture
Composition of binary relations can be decomposed into two operations: $latex \otimes$ and $latex \mathrm{dom}$: $latex g \otimes f = \left\{ ( ( x ; z) ; y) \, | \, x f y \wedge y g z \right\}$. Composition of binary relations is decomposed as: $latex g \circ f = \mathrm{dom} (g\otimes f)$. I […]