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What are projectives?

What are projectives? Here are some definitions.

Noun
  1. plural of projective
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Examples
There was no basis for expecting differences in the frequency of projectives or turnabouts as a function of partner.
The unimpressive evidence for validity and operational problems related to projectives led Reilly and Chao to a pessimistic conclusion regarding projectives.
In particular our assumptions hold if B is an abelian category with enough projectives.
By 2.2 we see that this is a full, contravariant imbedding, and by 2.3 the image of A in is a generating set of small projectives.
The projectives suggested considerable difficulty with women and a conflict between sexual preoccupation and hostility.

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