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cs.LO2024
Polynomial Universes in Homotopy Type Theory
C. B. Aberlé, David I. Spivak
Awodey, later with Newstead, showed how polynomial functors with extra structure (termed ``natural models'') hold within them the categorical semantics for dependent type theory. T…
math.CT2024
What kind of linearly distributive category do polynomial functors form?
David I. Spivak, Priyaa Varshinee Srinivasan
This paper has two purposes. The first is to extend the theory of linearly distributive categories by considering the structures that emerge in a special case: the normal duoidal c…
math.CT2024
A Polynomial Construction of Nerves for Higher Categories
Brandon T. Shapiro, David I. Spivak
We show that the construction due to Leinster and Weber of a generalized Lawvere theory for a familially representable monad on a (co)presheaf category, and the associated ``nerve'…