Co-equalizers and arbitrary co-limits exist in categories Fcd and Rld
I’ve uploaded a new version of my article “Equalizers and co-Equalizers in Certain Categories” (a very rough draft). In it is proved (among other) that arbitrary equalizers and co-equalizers of categories Fcd and Rld (continuous maps between endofuncoids and endoreloids) exist. I’ve proved earlier that in these categories there exist products and co-products. So now […]
Equalizers in certain categories
In this my rough draft article I construct equalizers for certain categories (such as the category of continuous maps between endofuncoids). Products and co-products were already proved to exist in my categories, so these categories are complete. In the above mentioned article I also claim co-equalizers (however have not yet proved that they are really […]
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 definitions of products and coproducts in certain categories
I have updated this article. It now contains a definition of product and coproduct for arbitrary morphisms of a dagger category every of Hom-sets of which is a complete lattice. Under certain conditions these products and coproducts are categorical (co)products for a certain category (“category of continuous morphisms”) having endomorphisms of the aforementioned category as […]
Product and co-product of endoreloids is now defined
Using this recently proved theorem I have defined product and co-product of endo-reloids. It is expressed by elegant algebraic formulas.
Direct products in a category of funcoids
I’ve released a draft article about categorical products and coproducts of endo-funcoids, as well as products and coproducts of other kinds of endomorphisms. An open problem: Apply this to the theory of reloids. An other open problem: Whether the category described in the above mentioned article is cartesian closed.
New concept: metamonovalued morphisms
Let fix some dagger category every of Hom-sets of which is a complete lattice, and the dagger functor agrees with the lattice order. I define a morphism $latex f$ to be monovalued when $latex \circ f^{-1}\le \mathrm{id}_{\mathrm{Dst}\, f}$. I call a morphism $latex f$ metamonovalued when $latex (\bigwedge G) \circ f = \bigwedge_{g \in G} […]
Crucial error in my definition of product funcoids
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 of coproduct.
The category Fcd has small co-products
Two 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 functors preserve co-products and whether my category has exponential objects and so is […]
The category of continuous maps between endofuncoids has small products
I have proved that Theorem The category of continuous maps between endofuncoids has small products. See my draft article for a proof.