  Relative theories(=closed subfunctors) are considered in exact, triangulated
and extriangulated categories by Dr\"{a}xler-Reiten-Smal{\o}-Solberg-Keller,
Beligiannis and Herschend-Liu-Nakaoka, respectively. We give a construction
method of closed subfunctors from given half exact functors which contains
existing constructions. Moreover, if an extriangulated category has enough
projective objects, then every closed subfunctor is obtained by this
construction.
