equivalences induced by functors

Question

I'm reading the paper Deriving Auslander's formula. In some parts of this paper, we can see equivalences which are induced by some functors. For example, at the end of the page 3, the author says: "the inclusion functor $~\mathsf{mod~C} \longrightarrow \mathsf{Mod~C}~$ induces an equivalence $$\mathsf{Ind~mod~C \overset{\sim} \longrightarrow Mod~C}$$". In general, how can we get an equivalence from a functor? are there any theorems? If yes, could you please give me some references for this subject? Thanks in advance.

$\mathsf{C}$ : A category (usually additive)
$\mathsf{Mod~C}$ : The category of additive functors $\mathsf{F:C^{OP} \longrightarrow Ab}$
$\mathsf{mod~C}$ : The category of finitely presented functors $\mathsf{F:C^{OP} \longrightarrow Ab}$
$\mathsf{Ind~mod~C}$ : The full subcategory of $\mathsf{((mod~C)^{OP},Ab)}$ consisting of functors which can be expressed as filtered colimits of representable ones.