# Quotient Presheaf inducing associated Sheaf

I have a question about the construction of the presheaf which induces the associated sheaf $\mathcal{K}_X ^* / \mathcal{O}_X ^*$ used for the definition of cartier divisors. By definition of quotient presheaf of $\mathcal{O}_X ^* \subset \mathcal{K}_X ^*$ is defined as follows: $U \to \mathcal{K}_X ^*(U) / \mathcal{O}_X ^*(U)$ for every open $U \subset X$.

I have two questions: Firstly: Why $\mathcal{O}_X ^* \subset \mathcal{K}_X ^*$ holds? (therefore $\mathcal{O}_X ^*(U) \subset \mathcal{K}_X ^*(U)$ for every U)?

And secondly: What kind of quotient structure is $\mathcal{K}_X ^*(U) / \mathcal{O}_X ^*(U)$? Quotient of what? Abelian groups?

Here the definitions of used symbols:

For (1), Definition 1.13 points out that $\mathcal O_X \subset \mathcal K_X$. Passing to sheaves of groups of units (which we can do on the level of presheaves if that's worrisome) is just a restriction of the domain of each localization map, so preserves injectivity.
Obviously if $\mathcal C$ lacks a forgetful functor to $\mathcal Ab$ you may need to be more careful, but even then you can often do things like one does for sheaves, which we might describe as a variation where rather than characterize exactness of a sequence in terms of its image under a forgetful functor to $\mathcal Ab$, we instead talk about its image under a (typically) infinite collection of less trivial functors to $\mathcal Ab$ (the stalk functors $\mathcal Sh_X \to \mathcal Ab$ which are indexed by the points of $X$), and require that the induced sequence of stalks be exact at every point.