Thin groupoid is an important but a heavily overlooked concept. When I did Google search for “thin groupid” (with quotes), I found just $latex {7}&fg=000000$ (seven) pages (and some of these pages were created by myself). It is very weird that such…

read moreTodd Trimble has notified me that he has written a “commentary” (notes) on my theory of funcoids presented in my monograph. His commentary is available at this nLab wiki page. I’ve started to read his notes. First I needed to lookup into…

read moreIn this short note I describe four sets (including the set of filters itself) which bijectively correspond to the set of filters on a poset. I raise the question: How to denote all these four posets and their principal elements? Please write…

read moreWhen I first saw topogenous relations at first I thought that my definition of funcoids was plagiarized (for some special case). But then I looked the year of publication. It was 1963, long before discovery of funcoids. Topogenous relations are a trivial…

read moreI have rewritten my draft article Products in dagger categories with complete ordered Mor-sets. Now I denote the product of an indexed family $latex X$ of objects as $latex \prod^{(Q)} X$ (instead of old confusing $latex Z’$ and $latex Z”$ notation) and…

read moreJust a few seconds ago I had an idea how to generalize both funcoids and reloids. Consider a precategory, whose objects are sets product $latex \times$ of filters on sets ranging in morphisms of this category operations $latex \mathrm{dom}$ and $latex \mathrm{im}$…

read moreI 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…

read moreI 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.

read moreThere 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….

read moreI’ve proved a new simple proposition about infimum product: Theorem Let $latex \pi^X_i$ be metamonovalued morphisms. If $latex S \in \mathscr{P} ( \mathsf{FCD} ( A_0 ; B_0) \times \mathsf{FCD} ( A_1 ; B_1))$ for some sets $latex A_0$, $latex B_0$, $latex A_1$,…

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