FOM: category theory, cohomology, group theory, and f.o.m.
Stephen G Simpson
simpson at math.psu.edu
Tue Feb 22 00:36:42 EST 2000
Reply to Todd Wilson's posting of Feb 21, 2000.
> I would propose that we acknowledge that the intuitions of
> category theorists concerning the fundamental nature of their subject,
> even in the absence of tangible results vindicating these intuitions,
> need not be a "mass hallucination", and instead make an honest attempt
> to discover whether there really is anything to them. For what it's
> worth, my own intuition tells me that there is, but I am not any
> closer to making this intuition explicit than the rest of the category
OK. I think there can be a reasonable compromise along these lines.
Category theorists have a strong intuition that adjoint functors are
``everywhere'', and I respect that intuition and the wealth of
examples that they adduce and would like to know what rigorous
principle underlies it. Still, I think we have to also agree that at
the present time the foundational interest of adjoint functors is far
from being well established.
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