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math.CT2025
Classifying strict discrete opfibrations with lax morphisms
Matteo Capucci, David Jaz Myers
We study discrete opfibration classifiers in enhanced 2-categories and show how, under suitable hypotheses, such classifiers can be endowed with the structure of a (lax or pseudo-)…
math.CT2024
Contextads as Wreaths; Kleisli, Para, and Span Constructions as 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…
math.CT2024
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…