  In this article, we study the heart of a cotorsion pairs on an exact category
and a triangulated category in a unified meathod, by means of the notion of an
extriangulated category. We prove that the heart is abelian, and construct a
cohomological functor to the heart. If the extriangulated category has enough
projectives, this functor gives an equivalence between the heart and the
category of coherent functors over the coheart modulo projectives. We also show
how an n-cluster tilting subcategory of an extriangulated category gives rise
to a family of cotorsion pairs with equivalent hearts.
