lift — Mathlib

English

There is a congruence between liftCochain φ α β h and liftCocycle φ α β h when one considers their projections to the appropriate components.

Русский

Существует согласованность между liftCochain φ α β h и liftCocycle φ α β h при проекции на нужные компоненты.

LaTeX

$$$\text{liftCochain}(φ, α, β, h) \equiv \text{liftCocycle}(φ, α, β, h) \text{ after projection}$$$

Lean4

/-- Given `φ : F ⟶ G`, this is the morphism `K ⟶ mappingCone φ` that is constructed
from a cocycle `α : Cochain K F 1` and a cochain `β : Cochain K G 0`
when a suitable cocycle relation is satisfied. -/
noncomputable def lift : K ⟶ mappingCone φ :=
  Cocycle.homOf (liftCocycle φ α β (zero_add 1) eq)

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