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.
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Algebraic general topology Category theory Filters General Topology Open problems Pointfree topology
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….
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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