I only know that category theory is some more rarified and
specialized type of group theory.  I'd like to hear how it might be
relevant.

Category theory isn't really a kind of group theory, it's better
thought of an alternative to set theory as a foundation for
mathematics...

It's relevant to the foundations of functional programming, for example....

Personally I don't think it's all that relevant to AGI engineering,
except insofar as an AGI system may use functional programming methods
for procedure representation.

However, I do think category theory might be a good tool for modeling
and interpreting the **emergent structures** that arise within a mind
-- reflexive awareness and all that...

OTOH, I can see how it might be possible to engineer a reasoning
system with category theory at the foundation....  An interesting
notion but IMO not necessary.

-- Ben

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