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Exemplar functors between categories QX and QY. (a) In category QX, there exist arrows for all possible object pairs (only three arrows are depicted here). In category QY, there are no arrows except for identity arrows for each object (not drawn). (b) One of 27 (=33) functors from QY to QX that preserve structures of QY. (c) One of three functors from QX to QY. This functor has to map all objects in QX into one object in QY and all arrows in QX to the identity arrow in QY
