Category Theory MOC

Commutative diagram

A commutative diagram is a directed graph with morphisms as edges and objects as vertices, such that any two paths sharing the same initial and final vertex are the same.¹ The diagram is thence said to commute.

As a functor

A diagram of shape in category is a functor , where is a usually Small category called the index category, cat and we typically use subscripts for objects. A diagram is called finite iff the index category is finite.

Related concepts are Cones and cocones, and then Limits and colimits.

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Footnotes

1. 2020, Topology: A categorical approach, p. 4 ↩