134 citations · 234 across the 10 of their papers we have counts for
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Sheaf Representations and Duality in Logic
Steve Awodey
The fundamental duality theories relating algebra and geometry that were discovered in the mid-20th century can also be applied to logic via its algebraization under categorical lo…
A proposition is the (homotopy) type of its proofs
Steve Awodey
An introduction and survey of homotopy type theory in honor of W.W. Tait.
Homotopy-initial algebras in type theory
Steve Awodey, Nicola Gambino, Kristina Sojakova
We investigate inductive types in type theory, using the insights provided by homotopy type theory and univalent foundations of mathematics. We do so by introducing the new notion…
Topos Semantics for Higher-Order Modal Logic
Steve Awodey, Kohei Kishida, Hans-Christoph Kotzsch
We define the notion of a model of higher-order modal logic in an arbitrary elementary topos . In contrast to the well-known interpretation of (non-modal) higher-order…
Scheme representation for first-order logic
Spencer Breiner
Although contemporary model theory has been called "algebraic geometry minus fields", the formal methods of the two fields are radically different. This dissertation aims to shrink…
First-Order Logical Duality
Steve Awodey, Henrik Forssell
From a logical point of view, Stone duality for Boolean algebras relates theories in classical propositional logic and their collections of models. The theories can be seen as pres…