2 citations · 2 across the 7 of their papers we have counts for
6 papers · 1 filter
Comonads as spaces
Aaron David Fairbanks, Kevin Carlson, David I. Spivak
Comonads on Set generalize both categories and topological spaces. Expanding upon Garner's work on ionads, we develop aspects of the theory of topological spaces for arbitrary como…
Interactions that reshape the interfaces of the interacting parties
David I. Spivak
Polynomial functors model systems with interfaces: each polynomial specifies the outputs a system can produce and, for each output, the inputs it accepts. The bicategory $\mathbb{O…
Categories by Kan extension
David I. Spivak
Categories can be identified -- up to isomorphism -- with polynomial comonads on Set. The left Kan extension of a functor along itself is always a comonad -- called the density com…
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…
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'…
Polynomial Functors: A Mathematical Theory of Interaction
Nelson Niu, David I. Spivak
This monograph is a study of the category of polynomial endofunctors on the category of sets and its applications to modeling interaction protocols and dynamical systems. We assume…