19. Tensor and Exterior algebras
We define the tensor product and the tensor algebra of a vector space. We then move onto its alternating cousin, the exterior algebra. Finally we apply the “metatheorem” from the previous lecture to transfer these linear algebra constructions to vector bundles.
We conclude with a rather lengthy digression on category theory, which culminates in a category-theoretic proof of said “metatheorem”. This is for interest only.
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