Editing Commutative diagram (section)

== In higher category theory ==
{{Main|Higher category theory}}

In higher category theory, one considers not only objects and arrows, but arrows between the arrows, arrows between arrows between arrows, and so on [[wiktionary:ad_infinitum|ad infinitum]]. For example, the category of small categories '''Cat''' is naturally a 2-category, with [[Functor|functors]] as its arrows and [[Natural transformation|natural transformations]] as the arrows between functors. In this setting, commutative diagrams may include these higher arrows as well, which are often depicted in the following style: <math>\Rightarrow</math>. For example, the following (somewhat trivial) diagram depicts two categories '''{{var|C}}''' and '''{{var|D}}''', together with two functors {{var|F}}, {{var|G}} : '''{{var|C}}''' → '''{{var|D}}''' and a natural transformation {{var|α}} : {{var|F}} ⇒ {{var|G}}:

:[[Image:2-commutative-diagram.svg|200px|class=skin-invert]]

There are two kinds of composition in a 2-category (called '''vertical composition''' and '''horizontal composition'''), and they may also be depicted via [[pasting diagrams]] (see [[2-category#Definitions]] for examples).