Triangulated category
Okay, so let's imagine you have a bunch of triangles. Each triangle has three sides, right?
Well, in math, a triangulated category is kind of like a bunch of triangles, but instead of sides, we have something called "objects."
These objects are connected with arrows, or "morphisms," which can point from one object to another.
The important thing about a triangulated category is that it follows certain rules. For example, you can "shift" the objects around (kind of like rotating them), and the arrows still make sense.
Also, if you have two arrows pointing in opposite directions, you can "cancel" them out, just like how -1 + 1 = 0. This is called a "cancellation property."
Overall, a triangulated category is just a special way of organizing a bunch of objects and morphisms so that they behave in a consistent and predictable way, kind of like how triangles always have three sides.
Well, in math, a triangulated category is kind of like a bunch of triangles, but instead of sides, we have something called "objects."
These objects are connected with arrows, or "morphisms," which can point from one object to another.
The important thing about a triangulated category is that it follows certain rules. For example, you can "shift" the objects around (kind of like rotating them), and the arrows still make sense.
Also, if you have two arrows pointing in opposite directions, you can "cancel" them out, just like how -1 + 1 = 0. This is called a "cancellation property."
Overall, a triangulated category is just a special way of organizing a bunch of objects and morphisms so that they behave in a consistent and predictable way, kind of like how triangles always have three sides.
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