# Non-concrete categories constructed from concrete categories

Can all non-concrete categories be constructed by taking a concrete category and identifying some of its morphisms?

Thanks

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Or rather: Given any category, can we find a suitable concrete category such that ... Personally, I doubt that. –  Hagen von Eitzen Dec 4 '12 at 10:06
All small categories are concrete. Categories that fail to be locally small cannot possibly be quotients of concrete categories, but it is possible to obtain non-locally-small categories by localising concrete categories. –  Zhen Lin Dec 4 '12 at 10:33