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.
Pullback pasting in an abelian category
Statement
Pullback pasting and pullback cancellation hold in every abelian category.
Facts & Assumptions
Given: A diagram of two adjacent commutative squares in an abelian category.
Pullback and pushout pasting hold in every category in which the relevant squares exist (Pullback and pushout pasting, with cancellation of the square adjacent to the outer edge).
Proof
An abelian category is still a category, and the statement only concerns pullback squares that already exist in that ambient category.
Therefore the general theorem [L1] applies verbatim to the abelian setting.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
3 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
- Emily Riehl, Category Theory in Context, Exercise 3.1.vi (standard reference, not scraped)