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Action

Defines Action, acts-on, group action
Requires
  • morphism

An action is one thing operating on another. A group acting on a set moves elements around. A function acting on an input produces an output. A debit acting on an account changes its balance.

In algebra, a group action is a way for a group G to move the elements of a set X around while respecting the group structure. The identity element does nothing. Composing two group elements and then acting is the same as acting with one and then the other.

More generally, an action is any morphism that takes an operator and a thing and produces a transformed thing. The operator does something to the thing. What “does something” means depends on the context — it could be rotation, translation, encryption, or posting a journal entry.

When this library uses acts-on as a predicate, the subject is an operation and the object is what it operates on.

Relations

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Referenced by

Cite

@misc{emsenn2026-action,
  author    = {emsenn},
  title     = {Action},
  year      = {2026},
  url       = {https://emsenn.net/library/math/terms/action/},
  publisher = {emsenn.net},
  license   = {CC BY-SA 4.0}
}