The category of finite-dimensional vector spaces, endowed with its usual tensor product, is rigid, that is it admits right and left duals. What happens in the infinite-dimensional case?
2026-04-24 02:23:24.1776997404
Rigid structure for the category of infinite-dimensional vector spaces
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Nothing good. No infinite dimensional vector space is isomorphic to its double dual in the linear algebraic sense, so there are no such vector spaces which admit duals in the categorical sense.