comp_counit_app — Mathlib

English

For adjunctions adj1 : F ⊣ G and adj2 : H ⊣ I, the counit of the composite adj1.comp adj2 is the composite of counits: (adj1.comp adj2).counit_X = H.map (adj1.counit_(I.obj X)) ≫ adj2.counit_X.

Русский

Единица композиции ковуньек равна композиции ковунек: (adj1.comp adj2).counit_X = H.map (adj1.counit_(I.obj X)) ≫ adj2.counit_X.

LaTeX

$$$ (adj_1 \cdot adj_2).counit_{X} = H.map (adj_1.counit_{(I.obj X)}) \circ adj_2.counit_{X} $$$

Lean4

@[simp, reassoc]
theorem comp_counit_app (X : E) :
    (adj₁.comp adj₂).counit.app X = H.map (adj₁.counit.app (I.obj X)) ≫ adj₂.counit.app X := by simp [Adjunction.comp]

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