Topology
《Topology》 · 第 33–34 页 · Chapter 3，Section 3.4–3.5
There is a unique homomorphism of $k$-algebras $\varepsilon \colon U \to k$ with $\varepsilon(E) = \varepsilon(F) = 0$ and $\varepsilon(K) = 1$. The following diagrams are commutative: $(\mathrm{id} \otimes \varepsilon) \circ \Delta = \mathrm{can}$, $(\varepsilon \otimes \mathrm{id}) \circ \Delta = \mathrm{can}$. The homomorphism $\varepsilon$ is called the counit (or augmentation) of $U$.