I have noticed a crucial error in the article with my definition of product funcoids (I confused the direction of an implication). Thus it is yet not proved that my “product” is really a categorical product. The same applies to my definition…
read moreI have put online a rough draft of an article about compact funcoids. In the draft article there is an error which I have trouble to find. I will pay $100 to the first person which finds my error (unless I find…
read moreI have added new section 16.13 “Relationships of cross-composition and subatomic products” with some important theorems (which I am going to use in the second volume of my book) to my preprint. I have also removed altogether the section “Displaced product” and…
read moreI’ve proved this conjecture. See my book (which also contains a pointfree version of this theorem).
read moreA new conjecture: Conjecture $latex \langle f \rangle \mathcal{X} = \bigsqcup_{F \in \mathrm{atoms}\, f} \langle F \rangle \mathcal{X}$ for every funcoid $latex f$ and $latex \mathcal{X} \in \mathfrak{F} (\mathrm{Src}\, f)$. This conjecture seems important for the notion of exponential object in the…
read moreTwo days ago I have proved that the category Fcd of continuous maps between endofuncoids has small products. Today I have also proved that this category has small co-products. The draft article is now available online. I’m yet to check whether product…
read moreI have proved that Theorem The category of continuous maps between endofuncoids has small products. See my draft article for a proof.
read moreI have quickly corrected the error in my proof of an important theorem. Now it is even more beautiful.
read moreThat 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.
read moreI 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…
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