# 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…

## 48 Citations

### Using the internal language of toposes in algebraic geometry

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It seems a worthy enterprise to trace the concept of adjunction back to the origins of the algebraic semantics of modal logic and to make explicit its ubiquity in this branch of mathematics.

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### Generalized Spaces for Constructive Algebra

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The purpose of this contribution is to give a coherent account of a particular narrative which links locales, geometric theories, sheaf semantics and constructive commutative algebra. We are hoping…

### Categorical and algebraic aspects of the intuitionistic modal logic IEL - and its predicate extensions

- PhilosophyJ. Log. Comput.
- 2021

The modal lambda calculus is constructed, which is Curry–Howard isomorphic to $\textbf{IEL}^{-}$ as the type-theoretical representation of applicative computation widely known in functional programming.

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