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
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Music: C418 - Pr Department