isoPointwiseLeftKanExtension — Mathlib

English

An isomorphism between the Day convolution of F and G and the pointwise left Kan extension of F.functor ⊠ G.functor along tensor

Русский

Изоморфизм между Day конволюцией F и G и точечным левым канлевским расслоением F.functor ⊠ G.functor вдоль tensor.

LaTeX

$$$ (F ⊗ G).functor \\cong (tensor C).pointwiseLeftKanExtension (F.functor ⊠ G.functor)$$$

Lean4

/-- An abstract isomorphism between `(F ⊗ G).functor` and the generic pointwise
left Kan extension of `F.functor ⊠ G.functor` along the -/
def isoPointwiseLeftKanExtension (F G : C ⊛⥤ V) :
    (F ⊗ G).functor ≅ (tensor C).pointwiseLeftKanExtension (F.functor ⊠ G.functor) :=
  Functor.leftKanExtensionUnique (F ⊗ G).functor (η F G) _
    ((tensor C).pointwiseLeftKanExtensionUnit (F.functor ⊠ G.functor))

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