On the Size of Categories

Peter Freyd and Ross Street

The purpose is to give a simple proof that a category is equivalent to a small category if and only if both it and its presheaf category are locally small.

Keywords: small, locally small, small homsets, idempotent, presheaf category.

AMS Classification (1991): 18A25.

Theory and Applications of Categories, Vol. 1, 1995, No. 9, pp 174-181.

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