What is the Grothendieck construction like?

Excellent blog d’un ancien élève de  John Baez, qui salue cet article sur Twitter

Joe Moeller

This is my best attempt at an intuitive introduction to the Grothendieck construction. I’ll give you the definition, but not before warming up to the idea. I’ll start with the earliest conceptual ancestor I could come up with: addition.

Numbers, Addition

What am I going to tell you about addition that you don’t already know? Nothing. I’m just going to frame it in a way that lends itself to the story I’m trying to tell.

What is addition? You take some numbers, a, b, and you make up a new number, called a+b. You could take a bunch of numbers $latex a_1, dots, a_n$ and make up a new number by repetition of the two-number version, call it $latex a_1 + dots + a_n$. Taking a bunch of numbers $latex a_1, dots, a_n$ is the same thing as a function $latex {1, dots, n} to mathbb N$.

Let k be…

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