The removal happened because I developed a more general and more beautiful theory.

The old version is preserved in Git history.

]]>But I noticed that these axioms do not fit into concrete examples which I am going to research.

So I have rewritten the text about restricted identities with somehow different axioms.

The theory of categories with restricted identities is presently presented in this rough draft not yet enough checked for errors. (I am going to move it to the main book after thorough examination.)

]]>Basically, a category with restricted identities is a category together with morphisms which are strictly less (in our order of morphisms) than identities . These “restricted identities” conform to certain axioms.

Using restricted identities, it is possible to turn a category into a semigroup, which I call “semigroup of unfixed morphisms”, because semigroups elements don’t have “fixed” source and destination objects, but describe common properties of morphisms with different sources and destinations (abstracting objects of the category away).

I wrote all this with the purpose to define “unfixed funcoids” and “unfixed reloids”, to allow abstract away the source and destination of say a funcoid, making it similar to “arbitrary binary relation” instead of limiting to binary relations between two given sets. This increases abstraction and may increase expressiveness. Particularly this allows to use just “set ” instead of “subset of our object “, that is it allows not to mention the objects for which the sets or filters are considered.

]]>I moved all research of unfixed filters to volume-1.pdf. Particularly now it contains subsections “The lattice of unfixed filters” and “Principal unfixed filters and filtrator of unfixed filters”.

Now I am going to research unfixed reloids and unfixed funcoids (yet to be defined).

]]>It is a trivial result but I had a weaker theorem in my book before today.

]]>Participate in writing my math research book (volumes 1 and 2), a groundbreaking general topology research published in the form of a freely downloadable book:

- implement existing ideas, propose new ideas
- develop new theories
- solve open problems
- write and rewrite the book and other files
- check for errors
- help with book LaTeX formatting
- represent the research at scientific conferences

You can do all of the above or any particular thing, dependently on your mood.

Required skills:

- basic general topology
- LaTeX
- Git

More desired skills:

- advanced general topology

the base of every primary filtrator over a distributive lattice which is an ideal base is a co-frame.

Really it can be not a complete lattice, as in the example of the lattice of the poset of all small (belonging to a Grothendieck universe) sets.

I will update my book soon.

]]>The theorem is in the subsection “The diagram for unfixed filters”.

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