Jim suggested this text:
> Paulo Perrone, Notes on Category Theory with examples from basic mathematics (2020)

This has a very good introduction for scientists and engineers interested in data-flow approaches. Coincidental that Perrone chooses a rare construction to introduce a composite

> ![](http://imageshack.com/a/img923/8991/QaxMhz.png)

The highlighted text is rare because the units of the inner and outer terms both have to be in radians. I have been using this formulation in the ENSO&QBO Azimuth Forum thread where it comes out of a Navier-Stokes LTE closed-form solution.

This is the composite data-flow:

![](https://imagizer.imageshack.com/img924/8215/ycXSL8.png)

I mentioned a possible connection to applied Category Theory in this earlier comment:
https://forum.azimuthproject.org/discussion/comment/21098/#Comment_21098

Where else this sin(cos(x)) formulation comes up in is in [Mach-Zehnder modulation](https://en.wikipedia.org/wiki/Mach%E2%80%93Zehnder_interferometer), where the physical data flow is described by a beam splitter, which mathematically transforms into a composite of a sinusoidally modulated inner phase term.

> ![](https://www.researchgate.net/profile/Deepak_Sharma185/publication/319738972/figure/fig4/AS:538712769810432@1505450541525/Block-diagram-of-Mach-Zehnder-modulator.png)

more detail here: https://geoenergymath.com/2020/03/02/australia-bushfire-causes/