Dialogue categories and chiralities
Summary: In this paper, we consider a two-sided notion of dialogue category which we call dialogue chirality and which we formulate as an adjunction between a monoidal category \(\mathcal{A}\) of proofs and a monoidal category \(\mathcal{B}\) of counter-proofs equivalent to its opposite category \(\mathcal{A}^{\mathrm{op}(0,1)}\). The two-sided formulation of dialogue categories is compared to the original one-sided formulation by exhibiting a 2-dimensional equivalence between a 2-category of dialogue categories and a 2-category of dialogue chiralities. The resulting coherence theorem clari es in what sense every dialogue chirality may be stricti ed to an equivalent dialogue category.
Cartesian closed categories and chiralities
scientific article; zbMATH DE number 6669846