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Telescope Equivalence

Abstract

The saved telescope and the saved ordinary cellular colimit are quasi-isomorphic for every arbitrary unbounded input. New proofs, released under the Apache 2.0 license.

Theorem 1.1 (solid Cellular Telescope To Colimit quasi Iso).

Lean statement: D5/S3/HomologicalAlgebra/Solid/TelescopeEquivalence.solidCellularTelescopeToColimit_quasiIso

Proof. Machine-checked in Lean as D5/S3/HomologicalAlgebra/Solid/TelescopeEquivalence.solidCellularTelescopeToColimit_quasiIso (✓ std3). ∎

Source. Repository-derived.

Commentary.

The actual mapping telescope is quasi-isomorphic to the actual cellular colimit, for every input and every integer homology degree.

Theorem 1.2 (solid Cellular Telescope homology solid).

Lean statement: D5/S3/HomologicalAlgebra/Solid/TelescopeEquivalence.solidCellularTelescope_homology_solid

Proof. Machine-checked in Lean as D5/S3/HomologicalAlgebra/Solid/TelescopeEquivalence.solidCellularTelescope_homology_solid (✓ std3). ∎

Source. Repository-derived.

Commentary.

The telescope itself is now genuinely derived-local.

References