tensorHom_def — Mathlib

English

The morphism tensorHom f g is defined by whiskering f and g with the appropriate factors: tensorHom f g equals whiskerRight f Y1 followed by whiskerLeft X2 g.

Русский

Гомоморфизм tensorHom f g задаётся как журавльный ответ: он равен whiskerRight f Y1 затем whiskerLeft X2 g.

LaTeX

$$$\text{tensorHom } f g = \text{whiskerRight } f Y_1 \; \gg \; \text{whiskerLeft } X_2 g.$$$

Lean4

theorem tensorHom_def {X₁ X₂ Y₁ Y₂ : GradedObject I C} (f : X₁ ⟶ X₂) (g : Y₁ ⟶ Y₂) [HasTensor X₁ Y₁] [HasTensor X₂ Y₂]
    [HasTensor X₂ Y₁] : tensorHom f g = whiskerRight f Y₁ ≫ whiskerLeft X₂ g := by
  rw [tensorHom_comp_tensorHom, id_comp, comp_id]

Похожие утверждения