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Definition

A concrete precategory $C$ is a precategory with a type $El(A)$ for every object $A:Ob(C)$ and a function $(-)((-)): Hom(A,B) \times El(A) \to El(B)$ for objects $A:Ob(C)$ and $B:Ob(C)$.

See also

• family of objects in a concrete precategory
• concrete category
• HilbR
• ETCS?