  In this article, we show that the localization of an extriangulated category
by a multiplicative system satisfying mild assumptions can be equipped with a
natural, universal structure of an extriangulated category. This construction
unifies the Serre quotient of abelian categories and the Verdier quotient of
triangulated categories. Indeed we give such a construction for a bit wider
class of morphisms, so that it covers several other localizations appeared in
the literature, such as Rump's localization of exact categories by biresolving
subcategories, localizations of extriangulated categories by means of Hovey
twin cotorsion pairs, and the localization of exact categories by two-sided
admissibly percolating subcategories.
