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math.CT2026
Comonads as spaces
Aaron David Fairbanks, Kevin Carlson, David I. Spivak
The paper develops a theory linking comonads on Set to topological spaces, introducing density comonads as abstract subbases and showing how every comonad yields an underlying spac…
math.CT2026
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…
math.CT2025
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…