Dialogue Categories and Chiralities
Paul-André Melliès
Université Paris Diderot - Paris 7, France
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Abstract
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 of proofs and a monoidal category of counter-proofs equivalent to its opposite category . 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 clarifies in what sense every dialogue chirality may be strictified to an equivalent dialogue category.
Cite this article
Paul-André Melliès, Dialogue Categories and Chiralities. Publ. Res. Inst. Math. Sci. 52 (2016), no. 4, pp. 359–412
DOI 10.4171/PRIMS/185