• Corpus ID: 2337874

QUANTIFIERS AND SHEAVES by

@inproceedings{Lawvere2010QUANTIFIERSAS,
  title={QUANTIFIERS AND SHEAVES by},
  author={F. William Lawvere},
  year={2010}
}
The unity of opposites in the title is essentially that between logic and geometry, and there are compelling reasons for maintaining that geometry is the leading aspect. At the same lime, in the present joint work with Myles Tierney there are important influences in the other direction: a Grothendieck " topology " appears most naturally as a modal operator, of the nature " it is locally the case that ", the usual logical operators such as V, 3, => have natural analogues which apply to families… 

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References

SHOWING 1-3 OF 3 REFERENCES

— On contradiction. Where do correct ideas come from? Peking

  • — On contradiction. Where do correct ideas come from? Peking
  • 1966

Equality in Hyperdoctrines and the Comprehension Scheme as an Adjoint Functor

  • LAWVERE. — Adjointness in Foundations (Dialectica) Proc. of A.M. S. Symposium on Pure Math. XVII-Applications of Category Theory
  • 1969