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math.CT2026
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…
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…