section exhibits two large categories that are not concretizable.

Remarks

Contrary to intuition, concreteness is not a property that a category may or may not satisfy, but rather a structure with which a category may or may not be equipped. In particular, a category C may admit several faithful functors into Set. Hence there may be several concrete categories (C, U) all corresponding to the same category C.

In practice, however, the choice of faithful

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