  A natural generalization of locally noetherian and locally coherent
categories leads us to define locally type $FP_{\infty}$ categories. They
include not just all categories of modules over a ring, but also the category
of sheaves over any concentrated scheme. In this setting we generalize and
study the absolutely clean objects recently introduced in a paper of
Bravo-Gillespie-Hovey. We show that $\mathcal{D}(\mathcal{AC})$, the derived
category of absolutely clean objects, is always compactly generated and that it
is embedded in $K(Inj)$, the chain homotopy category of injectives, as a full
subcategory containing the DG-injectives. Assuming the ground category
$\mathcal{G}$ has a set of generators satisfying a certain vanishing property,
we also show that there is a recollement relating $\mathcal{D}(\mathcal{AC})$
to the (also compactly generated) derived category $\mathcal{D}(\mathcal{G})$.
Finally, we generalize the Gorenstein AC-injectives of Bravo-Gillespie-Hovey,
showing that they are the fibrant objects of a cofibrantly generated model
structure on $\mathcal{G}$.
