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group homomorphisms. A proof of this is as follows: The set of morphisms from the symmetric group of order three to itself, , has ten elements: an element whose product on either side with every element of is (the homomorphism sending every element to the identity), three elements such that their product on one fixed side is always itself (the projections onto the three subgroups of order two), and six automorphisms. If were an additive category, then this set of ten elements would be a ring.

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