automatically add Global` to $ContextPath for all notebooks when using CellContext->Notebook

Question

I have some definitions in my init.m. E.g. my init.m contains this:

hex[n_]:=BaseForm[n,16];

I know that Mathematica puts this in the Global` context, and in a default configuration, each notebook's $Context is Global` and its $ContextPath also contains Global`. So my definitions are automatically available in any notebook I create.

However, I prefer the CellContext->Notebook option so each of my notebooks automatically gets its own private context. The problem is that this option (obviously) changes $Context to something other than Global`, and it also removes Global` from $ContextPath. So my init.m definitions are not automatically available in any notebook I create.

Now, I could type Global`hex when I want to use my hex function, or I could do AppendTo[$ContextPath, "Global`"] in each notebook. But I would rather have Global` added to each notebook's $ContextPath automatically.

Is there a way to get Global` into each notebook's $ContextPath automatically? Or is there some other way I can make my personal definitions available to each notebook automatically while using the CellContext->Notebook option?

Answer 1

This question seems to be slightly different from Globally loading packages while using a CellGroup as the default context (which I just posted an answer for).

Probably the simplest method would be to define your init.m functions in the System` context itself as this is always accessible no matter the CellContext. For example:

System`hex[n_] := BaseForm[n, 16]

Arguably it is not the best practice but if you are strict about starting all function names with lower-case letters this should theoretically not cause any problems.

Another strategy would be to put all your custom functions in a package or custom context (e.g. MyTools`) and use CellProlog as described by Brett Champion in the question linked above to add this context to $ContextPath for all cells.