sheafComposeIso_hom_fac — Mathlib

English

The hom component equals whiskerRight of toSheafify composed with sheafifyIso, demonstrating a standard factorization.

Русский

Гом-компонент равен whiskerRight от toSheafify, затем композиция с sheafifyIso.

LaTeX

$$$ toSheafify J (P \otimes F) \; \;≫ \; (sheafifyComposeIso J F P).hom = whiskerRight (toSheafify J P) F $$$

Lean4

@[reassoc (attr := simp)]
theorem sheafComposeIso_hom_fac :
    toSheafify J (P ⋙ F) ≫ (sheafifyComposeIso J F P).hom = whiskerRight (toSheafify J P) F :=
  sheafComposeNatTrans_fac J F (sheafificationAdjunction J A) (sheafificationAdjunction J B) P

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