Today’s glossary provoked by Michael Spivak.

Below I’ve drawn two vector spaces connected by a linear homomorphism ƒ, plus a linear functional λ going to ℝ. After seeing these pictures I hope it’s easier to understand how the pullback ƒ* works.

Here’s one of the main pictures for flavour:

Also, you can probably just skim the pictures and get the point (especially the Number Field one and the final one). That’s the fastest way to read this post.

Start with an abstract 𝓥ector space.

I’ll do some violence because I’ll need coordinates in a minute.