Direct limit

Imagine you have a bunch of toy blocks, some red and some blue, and you want to arrange them all in a line from left to right. Now imagine that some of the blocks have arrows pointing to other blocks in the line, as if to say "put me next to that block" or "I come after that block."

A direct limit is a way of taking all of those blocks and arrows and putting them together in a special way so you end up with one big line that incorporates all of the information from the individual blocks and arrows.

It's like taking a bunch of different paths and combining them into one big path that takes you everywhere you wanted to go.

Mathematicians use direct limits to help them study more complicated structures, like shapes with lots of twists and turns or even entire universes made up of different kinds of mathematical objects. It's a way of working with lots of pieces and parts to create something beautiful and complex.