Implicit Structure of Concrete Categories
Given a concrete category (C,U) and a cardinal number N, let UN be the functor C → Set determined by UN(c) = (U(c))N. Then a subfunctor of UN is called an N-ary predicate and a natural transformation UN → U an N-ary operation.
The class of all N-ary predicates and N-ary operations of a concrete category (C,U), with N ranging over the class of all cardinal numbers, forms a large signature. The category of models for this signature then contains a full subcategory which is equivalent to C.
Read more about this topic: Concrete Category
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