I reflect on scalar nature so my question is very simple: what are $\textit{scalars}$, really ?
I read about ground ring
There are also generalisations in which k might be, for example, a monad. It is also important to consider base change from one ground ring to another, mediated by a ring homomorphism or even a bimodule.
The elements of the ground ring (or base ring) are called scalars but this is like saying, from an inverse operation point of view, that a monad is division rings of scalars or subring of scalar matrices or as semiring.
I read also an interesting paper Scalars, Monads, and Categories that says
These interrelations will be expressed in terms of “triangles of adjunctions”, involving for instance various kinds of monoids (non-commutative, commutative, involutive).
If we can use K-enriched category to rewrite scalar structure definition ..
Every $K$-enriched category $C$ has an underlying ordinary category, usually denoted $C_0$, defined by $C_0(x,y) = K(I, hom(x,y))$ where $I$ is the unit object of $K$.
.. what are $\textit{scalars}$, really ?