K-theory and sets
martdowd at aol.com
martdowd at aol.com
Sat Jun 4 11:21:36 EDT 2022
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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