Category

  1. Collection of objects (e.g. A, B, C, …)
  1. Collection of arrows (morphisms) between the objects (f : A → B, g : B → C)
  1. Composition of arrows (e.g. h = g o f : A → C)
Under the following rules:
  1. f o (g o h) = (f o g) o h
    (The composition of morphisms needs to be associative)
  1. f o idA = f = idB o f
    (The identity morphism/Unit)
Where idX is the identity function (idX : X → X) so that idX(x) = x, where x ∈ X.

Here is a list of other group-like structures and their properties:
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