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

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