Alphabeta MathHow 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.
Equivalence of extensions is an equivalence relation
Statement
Equivalence of extensions with fixed endpoints is an equivalence relation.
Facts & Assumptions
Given: Extensions with the same subobject and quotient.
Proof
Identity maps give reflexivity, and composing endpoint-identity maps of short exact sequences gives transitivity.
Such a map is an isomorphism on the middle term; its inverse commutes with the endpoint maps, so it witnesses symmetry.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
4 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Charles A. Weibel, An Introduction to Homological Algebra, Chapters 3–4 (standard reference, not scraped)