K-theory and sets

[martdowd at aol.com]

FOM:
Ignacio Anon wrote: 

 it might be interesting to note that things like K-theory and the index theorem, were developed by Atiyah, Bott and others, in their attempt to translate into simple topology, Grothendieck's new, foundational, algebraic perspective on the Riemann-Roch theorem.
 
 A good example of what category theory has done for mathematics is the notion of adjoint functors.  The wikidedia article  https://en.wikipedia.org/wiki/Adjoint_functorshas a survey.  Galois didn't know any category theory (or probably much partial order theory), but he discovered an important Galois adjunction.

Martin Dowd
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