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math.CT2026
Twisted double functors and loosely discrete opfibrations
Michael Lambert, David Jaz Myers, Evan Patterson
Various situations in the theory and applications of double categories, ranging from a loose Yoneda theory and loose compact closure to double-operadic systems theory, require a no…
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…