Definition islunit_cat {L} (f : C⟦L ⊗ L,L⟧) (u : C⟦TC,L⟧) : UU := ι · (u ×× 1) · f = 1.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.Algebra.Monoids. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.OrderTheory.Lattice.Bounded. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Terminal.