  In this paper, we consider a kind of ideal quotient of an extriangulated
category such that the ideal is the kernel of a functor from this
extriangulated category to an abelian category. We study a condition when the
functor is dense and full, in another word, the ideal quotient becomes abelian.
Moreover, a new equivalent characterization of cluster-tilting subcategories is
given by applying homological methods according to this functor. As an
application, we show that in a connected 2-Calabi-Yau triangulated category B,
a functorially finite, extension closed subcategory T of B is cluster tilting
if and only if B/T is an abelian category.
