4 papers · 1 filter
Contextful Arrows via Wreath Products
Matteo Capucci, David Jaz Myers
We introduce contextads and the Ctx construction, unifying various structures and constructions in category theory dealing with context and contextful arrows---comonads and their K…
Algorithmic and Extremal Obstructions Through the Language of Cohomology
Anny Beatriz Azevedo, Benjamin Merlin Bumpus, Matteo Capucci +2
We model problems as presheaves that assign sets of certificates to input instances, and we show how to use presheaf Čech cohomology to capture the precise ways in which local solu…
On Quantifiers for Quantitative Reasoning
Matteo Capucci
We explore a kind of first-order predicate logic with intended semantics in the reals. Compared to other approaches in the literature, we work predominantly in the multiplicative r…
Organizing Physics with Open Energy-Driven Systems
Matteo Capucci, Owen Lynch, David I. Spivak
Organizing physics has been a long-standing preoccupation of applied category theory, going back at least to Lawvere. We contribute to this research thread by noticing that Hamilto…