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Posts about double dual.

A standard topic in linear algebra is the dual space of a vector space, as well as the canonical embedding of a vector space in its double dual. Moreover, transposition of homomorphisms in terms of dual spaces is rather well known. Something less known is that one has a canonical map from the dual of V tensored with W to the space of homomorphisms from V to W. In this abstract nonsense post, we describe these canonical maps, their interplay, and try to determine their images.