Integral object of a category

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A name introduced by S. MacLane [a1] (and now largely obsolete) for a special kind of generator of a category. Explicitly, an integral object is a generator which is "minimal" in the sense that it has no non-trivial idempotent endomorphisms. The name derives from the fact that the unique integral object in the category of Abelian groups is the group of integers.


[a1] S. MacLane, "Duality for groups" Bull. Amer. Math. Soc. , 56 (1960) pp. 485–516
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