Definition. A prolinear category is a category endowed with two promonoidal structures, and , and two frobenius natural isomorphisms relating them
& \left(∫^{W} ℂ(A ; C ⅋ W) × ℂ(W ⊗ B ; D) \right) \overset{ϕ₁}→ ℂ(A ⊗ B; C ⅋ D), \\ & \left(∫^{W} ℂ(A ⊗ W ; C) × ℂ(B ; W ⅋ D) \right) \overset{ϕ₁}→ ℂ(A ⊗ B; C ⅋ D), \end{aligned}$$ such that every formal equation out of these frobenius isomorphisms and the coherence isomorphisms of the promonoidal categories holds. - [polycategory](notes/pieces/polycategory.md) - [Prolinear contour](notes/pieces/Prolinear%20contour.md) - [Virtual stars](notes/pieces/Virtual%20stars.md) - [Prolinear category of spliced arrows](notes/pieces/Prolinear%20category%20of%20spliced%20arrows.md)