English
There is a natural isomorphism between the composite inl_D_E ∘ inr_C(D ⊕ E) ∘ inverseAssociator_{C D E} and inr_C D ∘ inl_(C ⊕ D) E, obtained by whiskering and sum-composition with the inverse associator. In symbols, inl_D E ∘ inr_C(D ⊕ E) ∘ inverseAssociator_{C D E} ≅ inr_C D ∘ inl_(C ⊕ D) E.
Русский
Существует естественное изоморождение между составом inl_D E ∘ inr_C(D ⊕ E) ∘ inverseAssociator_{C D E} и inr_C D ∘ inl_(C ⊕ D) E, полученное при помощи whiskering и суммы.
LaTeX
$$$$\mathrm{inl}_{D E} \circ \mathrm{inr}_{C}(D\oplus E) \circ \mathrm{inverseAssociator}_{C D E} \cong \mathrm{inr}_{C D} \circ \mathrm{inl}_{(C D) E}.$$$$
Lean4
/-- Further characterizing the composition of the inverse of the associator and the right
inclusion. -/
@[simps!]
def inlCompInrCompInverseAssociator : inl_ D E ⋙ inr_ C (D ⊕ E) ⋙ inverseAssociator C D E ≅ inr_ C D ⋙ inl_ (C ⊕ D) E :=
isoWhiskerLeft (inl_ _ _) (inrCompInverseAssociator C D E) ≪≫ Functor.inlCompSum' _ _
