diagram

Idea

• : some objects connected by some morphisms in a category \(C\)
• we draw diagrams by drawing some objects (or dots labeled by objects) connected by arrows labeled by morphisms.
• the concept is often used when talking about (co)limits - we say "the limit or colimit of a diagram"

• two natural ways to formally define diagram
  • 1. a functor, with a (very) small category as domain
  • 2. a functor, with a free category as domain
    • we draw a directed graph, it freely generates a category

Definition

• ...

from Topology - A Categorical Approach Simply put, a diagram is a visualization of morphism composition. A commutative diagram is a visualization of equalities between compositions.