I am attempting to define direct products in the category cont(mepfFcd) (the category of monovalued, entirely defined continuous pointfree funcoids), see this draft article for a definition of this category. A direct product of objects may possibly be defined as the cross-composition…

read moreI started to write a new article Categories related with funcoids. It is now a very preliminary partial draft.

read moreFrom 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…

read moreThe following is an important question related with categories related with funcoids: Question Is every isomorphisms of the category of funcoids a discrete funcoid?

read moreIn my draft article Multifuncoids there was a serious error. I defined funcoidal product wrongly. Now a new version of the article (with corrected error) is online.

read moreI have solved the first two of these three open problems I proposed, but have no clue how to solve the third. (Actually, I’ve solved only a special case of the second problem, but that’s OK, this special case is enough for…

read moreSee here (especially this draft article) for definition of cross-composition product and quasi-cartesian functions. Conjecture 1 Cross-composition product (for small indexed families of relations) is a quasi-cartesian function (with injective aggregation) from the quasi-cartesian situation $latex {\mathfrak{S}_0}&fg=000000$ of binary relations to the…

read more