splice-contour adjunction

Last updated Apr 23, 2024

Splice-Contour adjunction refers to a family of adjunctions that compute some form of context out of a categorical structure. An explicit example and the name are in the work of Mellies and Zeilberger, who apply the adjunction to parsing.

• The contour of a multicategory is left adjoint to the multicategory of spliced arrows, this produces an adjunction between multicategories and categories. The promonoidal contour is left adjoint to the promonoidal category of spliced arrows. This produces an adjunction between promonoidal categories and categories.
• The contour of a polycategory is left adjoint to the spliced arrow polycategory. The contour of a prostar autonomous category is left adjoint to the spliced arrow prostar autonomous category.
• There exists also a message splice-contour adjunction.
• optical contour is left adjoint to the multicategory of raw optics.