3 papers
math.CT2026
Free Doubly-Infinitary Distributive Categories are Cartesian Closed
Fernando Lucatelli Nunes, Matthijs Vákár, Matthijs Vákár
We study the composite free completion Dist(C) := Fam(Fam(C^op)^op), obtained by first freely adjoining small products and then freely adjoining small coproducts. A natural pseudod…
math.CT2025
Monoidal closure of Grothendieck constructions via -tractable monoidal structures and Dialectica formulas
Fernando Lucatelli Nunes, Matthijs Vákár
We examine the categorical structure of the Grothendieck construction of an indexed category . Our a…
math.CT2024
Free extensivity via distributivity
Fernando Lucatelli Nunes, Rui Prezado, Matthijs Vákár
We consider the canonical pseudodistributive law between various free limit completion pseudomonads and the free coproduct completion pseudomonad. When the class of limits includes…