DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (deepseek-v4-pro + gpt-5.6-terra)audited 2026-08-16

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Lifts of maps, paths, and homotopies through a covering map

Definition

Let $p : E \to B$ be a covering and $f : Y \to B$ continuous. A lift of $f$ through $p$ is a continuous map $\tilde{f} : Y \to E$ with $p \circ \tilde{f} = f$ . This includes lifts of paths $I \to B$ and of homotopies $Y \times I \to B$ ; an initial lift prescribes the restriction at time $0$ (Homotopies of continuous maps, homotopies relative to a subspace, and path homotopies relative to the endpoints, Paths, path-connected spaces and path components).

Depends on

Used by

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 55 results over 13 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.

Sources

Allen Hatcher, Algebraic Topology, §1.3 (standard reference, not scraped)
J. Peter May, A Concise Course in Algebraic Topology, Ch. 3 (standard reference, not scraped)
Marco Gualtieri, MAT1300 Week 4 Term 2, §1.6 (standard reference, not scraped)