What is $\text{Hom}_{R\text{-Alg}}(R^{\overline{R}(B)},C)\rightarrow \overline{C}(B)$?

67 Views Asked by At

I'm reading this Synthetic Differential Geometry and don't understand (A.1) on page 213.

$\text{Hom}_{R\text{-Alg}}(R^{\overline{R}(B)},C)\xrightarrow{\nu _{B,C}} \overline{C}(B)$ (A.1)

Would you give me a comprehensible explanation of this $\nu_{B,C}$?

I might understand.

Let $S$ be the functor $\text{Hom}_{R\text{-Alg}}(R^{\overline{R}(-)},C):\text{FP}\mathbb{T}^{op} \rightarrow \mathcal{E}$. I want to define $S\xrightarrow{\nu_{C}}\overline{C}$, however, it is suffice to define $S\circ F\rightarrow C$.