I've tried to reduce my problem to the following set-up and question:
Say we have algebraic structures A and B (think of groups) constructed
like this:
A = CreateGroup('alpha')
B = CreateGroup('beta')
Elements are then
a = A.an_element()
b = B.an_element()
Now I want to perform a binary operation on a and b, e.g.
c = a * b
Thus, the coercion model has to find a parent where both live in (there
is no coercion from A to B or vice versa).
I have a common parent C which can be created from A and B:
C = PlugTogether(A, B)
(think here of something similar to a cartesian product). This parent C
is what we want to find, but how can the coercion model do this? How can
it discover this PlugTogether construction?
I've read about functorial constructions, but are these here the key? If
yes, how does this work (since there are two groups involved)?
Best wishes
Daniel
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