standard — Mathlib

English

The Ext functor Ext(X,Y,n) is defined as a SmallShiftedHom in the derived framework.

Русский

Функтор Ext(X,Y,n) задаётся как SmallShiftedHom в рамках производной конструкции.

LaTeX

$$$\operatorname{Ext}(X,Y,n) = \operatorname{SmallShiftedHom}(\mathrm{HomologicalComplex.quasiIso}(C,(\text{ComplexShape.up }\mathbb{Z})), (\mathrm{CochainComplex.singleFunctor} C 0).obj X, (\mathrm{CochainComplex.singleFunctor} C 0).obj Y, n)$$$

Lean4

theorem standard : HasExt.{max u v} C := by
  letI := HasDerivedCategory.standard
  exact hasExt_of_hasDerivedCategory _

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