ActionCategory — Mathlib

English

Objects of the action category M ⟲ X correspond to elements of X, via the isomorphism X ≃ ActionCategory M X.

Русский

Объекты категории действия M↦X соответствуют элементам X через экивалентность X ≃ ActionCategory M X.

LaTeX

$$$X \cong ActionCategory M X$$$

Lean4

/-- A multiplicative action M ↻ X induces a category structure on X, where a morphism
from x to y is a scalar taking x to y. Due to implementation details, the object type
of this category is not equal to X, but is in bijection with X. -/
def ActionCategory :=
  (actionAsFunctor M X).Elements

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