objects $d \in C$ such that $C(d,-)$ commutes with certain
,
A functor
is a $\kappa$-accessible functor (for $\kappa$ a regular cardinal) if $C$ and $D$ are both $\kappa$-accessible categories and $F$ preserves $\kappa$-filtered colimits. $F$ is an accessible functor if it is $\kappa$-accessible for some regular cardinal $\kappa$.
The theory of accessible 1-categories is described in
Society, Rhode Island, 1989.1989.
The theory of accessible $(\infty,1)$-categories is the topic of section 5.4 of
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