instIsCommComonObjOfCartesian — Mathlib

English

For F: C ⥤ D and a natural isomorphism η: G ≅ H, the core of the left whiskering of η by F equals the composite of the cores as stated: (isoWhiskerLeft F η).core = F.coreComp G ≪≫ isoWhiskerLeft F.core η.core ≪≫ (F.coreComp H).symm.

Русский

Для функторов F: C ⥤ D и изоморфизма η: G ≅ H ядро левого whiskerLeft по η эквивалентно сложению ядер: …

LaTeX

$$$ (\\mathrm{isoWhiskerLeft}\\ F\\eta).\\mathrm{core} = F.\\mathrm{coreComp} G \\;\\ll≫\\; \\mathrm{isoWhiskerLeft} F.\\mathrm{core} \\eta.\\mathrm{core} \\;\\ll≫\\; (F.\\mathrm{coreComp} H).\\mathrm{symm} $$$

Lean4

/-- Every object in a cartesian category has commutative comonoid structure. -/
instance instIsCommComonObjOfCartesian (X : C) : IsCommComonObj X where

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