"new foundations must give new math"

from "The Basic Picture. Structures for constructive topology"

by Giovanni Sambin, Oxford University Press, forthcoming


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Abstracts » Dosen

Kosta Dosen

Modal Logic and Frobenius Algebras

It is well known that deductions involving only modalities in the modal logic S4 are closely connected with the categorial notions of monad and comonad.

When we pass to S5, we obtain a notion slightly more general than the notion of Frobenius monad, which underlies Frobenius algebras. Frobenius algebras play an important role in connection with topological quantum field theories.

The main result in this area, which may be understood as a categorial coherence theorem that gives a geometrical description of the free commutative Frobenius monad via cobordisms in dimension 2, is based on more general analogous geometrical coherence results for deductions involving the modalities in S5.