# Discussion of article "Category Theory in MQL5 (Part 7): Multi, Relative, and Indexed Domains"

New article Category Theory in MQL5 (Part 7): Multi, Relative, and Indexed Domains has been published:

Category Theory is a diverse and expanding branch of Mathematics which is only recently getting some coverage in the MQL5 community. These series of articles look to explore and examine some of its concepts & axioms with the overall goal of establishing an open library that provides insight while also hopefully furthering the use of this remarkable field in Traders' strategy development.

Formally though, A mapping of relative domains over N, represented as f: (E,π) à (E’,π’), is a function f: E àE’ such that the following triangle commutes

To illustrate this for traders we would exploit morphism f by modifying our square commute used above to be a simple tringle with no D domain. In exploiting f we would seek morphism weights between two domains E & E’ which for our demonstration purposes are, as above, multidimensional data at index zero and at index 1. The ‘multi-dimensionality’ simply means we are measuring and logging more than one data point. In our case this is changes in highs, and changes in lows. So because we already know the eventual change in price range for the bar at index 1 (our lag) we would use morphism f to transform our current data point whose eventual change we do not know yet and find which of the elements in E’ it is closest to matching. The closest match’s codomain element across π’ will give us our projected change.

Running tests as before does give us the following report.

Author: Stephen Njuki

Good work.

Kenneth Berry Cunningham #:
Good work.
Hi,
Am glad you liked it. Cheers.

" We have, this far, avoided referring to domains as sets but perhaps going forward in the next articles we will refer to them as sets since these are better understood while domains, though more appropriate since they are an umbrella term for other 'types of sets' like  topologies ,  simplical complexes , and other formats, we will not have such applications and examples in these series of articles. "

A pity that topologies and simplical complexes will not be considered.