
Re: Which term to choose?
Posted:
Oct 26, 2013 7:20 AM


William Elliot wrote:
> On Fri, 25 Oct 2013, William Elliot wrote: >> On Fri, 25 Oct 2013, Victor Porton wrote: >> >> > Which term is better for a concept which generalizes both embedding and >> > restriction: 1. "embeddingrestriction"; 2. "restrembedding"? >> > >> > ... or maybe "commonization"? >> >> Perhaps embedded restriction. >> How's it defined? >> >> What's your reloid distribution theorem? >> Please state it in ascii in the body of your reply. > > Is this it? Let F be a principle filter for XxY > and for all j in J, Gj a filter for YxZ. Then > . . F o /\_j Gj = /\{ F o Gj  j in J }. > > Also if F filter for XxY, G,H filter for YxZ, then > . . F o G/\H = FoG /\ FoH.
principle > principal
Yes, these two theorems are correct.
> Are there any additional distributive theorems for > reloids other than reversing the compositions?
I know no other distributive theorems of reloids.
However there is a conjecture, that composition with a complete (or cocomplete dependently on the side of composition) reloid is distributive. (Principal reloids are a special case of complete reloids.)
For the definition of complete reloids see my book: http://www.mathematics21.org/algebraicgeneraltopology.html
Well, there are also similar theorems for funcoids.

