In my lecture notes it says:
‘Complex representations of a given group G, together with intertwiners, form a category enriched over the complex numbers.’
Is it true that the category is enriched over the complex numbers? Why?
In a specific case this is true, namely: I know that by Schur’s lemma given a simple complex representation $M$ of a group $G$ any intertwiner $\phi$: $M$ $\rightarrow$ $M$ is a multiple of the identity. How to proceed from here?
As Tobias Kildetoft mentioned in the comments:
The expression ‘category enriched over the complex numbers’ refers to the ‘category enriched over the category of ℂ-vector spaces‘. This was not clear to me.
With that knowledge, the statement quoted above follows directly from the definitions.