Complete Derivation: Universal Property of the Tensor Product

Previous tensor product video: /watch/47_dnjBZSnKZd The universal property of the tensor product is one of the most important tools for handling tensor products. It gives us a way to define functions on the tensor product using bilinear maps. However, the statement of the universal property can be confusing if it is presented without background. This video is an explanation of the universal property that proves it for a concrete instantiation of the tensor product of vector spaces (or modules over a commutative ring). Tensor Products playlist: /playlist/PLug5ZIRrShJHCtzgzZyRqSdzr8wYlN2qk 0:00 Introduction 3:04 Constructing the Tensor Product 7:54 Bilinear Maps 10:39 Maps on the Tensor Product 16:17 Defining g 26:24 Linearity and Uniqueness 29:44 Universal Property 30:50 Example Subscribe to see more new math videos! Music: C418 - Pr Department

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