8 citations · 15 across the 10 of their papers we have counts for
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The Fundamental Theorem of Calculus point-free, with applications to exponentials and logarithms
Steven Vickers
Working in point-free topology under the constraints of geometric logic, we prove the Fundamental Theorem of Calculus, and apply it to prove the usual rules for the derivatives of…
Generalized point-free spaces, pointwise
Steven Vickers
We survey foundational principles of Grothendieck's generalized spaces, including a critical glossary of the various, and often conflicting, terminological usages. Known results us…
Point-free Construction of Real Exponentiation
Ming Ng, Steven Vickers
We define a point-free construction of real exponentiation and logarithms, i.e.\ we construct the maps $\exp\colon (0, \infty)\times \mathbb{R} \rightarrow \!(0,\infty),\, (x, ζ) \…
Fibrations of AU-contexts beget fibrations of toposes
Sina Hazratpour, Steven Vickers
Suppose an extension map in the 2-category of contexts for arithmetic universes satisfies a Chevalley criterion for being a…
Arithmetic universes and classifying toposes
Steven Vickers
Reasoning in the 2-category Con of contexts, certain sketches for arithmetic universes (i.e. list arithmetic pretoposes; AUs), is shown to give rise to base-independent results of…
Sketches for arithmetic universes
Steven Vickers
A theory of sketches for arithmetic universes (AUs) is developed. A restricted notion of sketch, called here "context", is defined with the property that every non-strict model is…
Geometric constructions preserve fibrations
Bertfried Fauser, Steven Vickers
Let be a representable 2-category, and a 2-endofunctor of the arrow 2-category such that (i) $\mathsf{cod} \mathfrak{T…
Gelfand spectra in Grothendieck toposes using geometric mathematics
Bas Spitters, Steven Vickers, Sander Wolters
In the (covariant) topos approach to quantum theory by Heunen, Landsman and Spitters, one associates to each unital C*-algebra, A, a topos T(A) of sheaves on a locale and a commuta…
The Born rule as structure of spectral bundles (extended abstract)
Bertfried Fauser, Guillaume Raynaud, Steven Vickers
Topos approaches to quantum foundations are described in a unified way by means of spectral bundles, where the base space is a space of contexts and each fibre is its spectrum. Dif…