mul_eq_mul — Mathlib

English

In a cartesian monoidal category, the multiplication μ of a monoid object M equals the product of the projections fst and snd from M × M to M, i.e., μ = fst ∘ snd viewed as arrows multiplied in the monoid structure.

Русский

В декартовом моноидальном kategorie умножение μ моноида M равно произведению проекций fst и snd из M × M в M: μ = fst ⋅ snd.

LaTeX

$$$ \\mu = (\\mathrm{fst}_{M,M}) * (\\mathrm{snd}_{M,M}) $$$

Lean4

theorem mul_eq_mul : μ = fst M M * snd _ _ :=
  show _ = _ ≫ _ by rw [lift_fst_snd, Category.id_comp]

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