  We consider an arbitrary Abelian category $\mathcal{A}$ and a subcategory
$\mathcal{T}$ closed under extensions and direct summands, and characterize
those $\mathcal{T}$ that are (semi-)special preenveloping in $\mathcal{A}$; as
a byproduct, we generalize to this setting several classical results for
categories of modules. For instance, we get that the special preenveloping
subcategories $\mathcal{T}$ of $\mathcal{A}$ closed under extensions and direct
summands are precisely those for which $(_{}^{\perp_1}\mathcal{T},\mathcal{T})$
is a right complete cotorsion pair, where $_{}^{\perp_1}\mathcal{T}:=\text{Ker}
(\text{Ext}_{\mathcal{A}}^1(-,\mathcal{T}))$. Particular cases appear when
$\mathcal{T}=V^{\perp_1}:=\text{Ker}(\text{Ext}_{\mathcal{A}}^1(V,-))$, for an
$\text{Ext}^1$-universal object $V$ such that $\text{Ext}_{\mathcal{A}}^1(V,-)$
vanishes on all (existing) coproducts of copies of $V$. For many choices of
$\mathcal{A}$, we show that these latter examples exhaust all the
possibilities.
  We then show that, when $\mathcal{A}$ has an epi-generator, the
(semi-)special preenveloping torsion classes $\mathcal{T}$ given by
(quasi-)tilting objects are exactly those for which any object
$T\in\mathcal{T}$ is the epimorphic image of some object in
$_{}^{\perp_1}\mathcal{T}$ (and the subcategory
$\mathcal{B}:=\text{Sub}(\mathcal{T})$ of subobjects of objects in
$\mathcal{T}$ is reflective) and they are, in turn, the right constituents of
complete cotorsion pairs in $\mathcal{A}$ (resp., $\mathcal{B}$).
  In a final section, we apply the results when
$\mathcal{A}=\mathrm{mod}\text{-}R$ is the category of finitely presented
modules over a right coherent ring $R$, something that gives new results and
raises new questions even at the level of classical tilting theory in
categories of modules.
