  We furnish any category of a universal (co)homology theory. Universal
(co)homologies and universal relative (co)homologies are obtained by showing
representability of certain functors and take values in $R$-linear abelian
categories of motivic nature, where $R$ is any commutative unitary ring.
Universal homology theory on the one point category yields "hieratic"
$R$-modules, i.e. the indization of Freyd's free abelian category on $R$.
Grothendieck $\partial$-functors and satellite functors are recovered as
certain additive relative homologies on an abelian category for which we also
show the existence of universal ones.
