Full Idea
There is an idea that objects belonging to the same category have the same criteria of identity. This view was first explicitly endorsed by Frege (1884), and was later systematized by Dummett (1981).
Gist of Idea
Maybe objects in the same category have the same criteria of identity
Source
Jan Westerhoff (Ontological Categories [2005], Intro)
Book Reference
Westerhoff,Jan: 'Ontological Categories' [OUP 2005], p.5
A Reaction
This approach is based on identity between equivalence classes. Westerhoff says it means, implausibly, that the resulting categories cannot share properties.