The ring hom $\mathbf{Z}\rightarrow A$ Let $A$ be a ring with idenity. Is there a standard notation for the canonical ring hom $\mathbf{Z}\rightarrow A$?
 A: $$\underline{~~~~\eta~~~~} $$
In a monoidal category, a monoid (or algebra) is a triple $(A,e,m)$, where $A$ is an object, $e : 1 \to A$ (unit) is a morphism and $m : A \otimes A \to A$ (multiplication) is a morphism such that $m \circ (m \otimes A) = m \circ (A \otimes m)$ (associativity) and $m \circ (e \otimes A) = \mathrm{id} = m \circ (A \otimes e)$ (unit axiom). For example, a ring is a monoid in the monoidal category of abelian groups, equipped with the usual tensor product $\otimes_{\mathbb{Z}}$ and with $1=\mathbb{Z}$. In this concise description of rings, the (multiplicative) unit element of the ring actually corresponds the unit morphism $e : \mathbb{Z} \to A$. Therefore, I would denote this morphism by $e$ (eins) or $1$ (one) or $u$ (unit). You can also stress the dependency of $A$ and write $e_A,1_A$ or $u_A$. You can also view monoids as special monads, and in this setting the unit is often denoted by $\eta$. This is done for example in Mac Lane's book and at the nlab. It is also quite standard in texts about bialgebras (in particular Hopf algebras), which are usually written as $(A,\eta,\mu,\varepsilon,\Delta)$, where $\eta$ is the unit, $\mu$ is the multiplication, $\varepsilon$ is the counit and $\Delta$ is the comultiplication.
So probably $\eta$ should be an "almost standard" notation.
