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.
Absolute colimits
Definition
A colimit of a diagram in a category is absolute when every functor with domain preserves that colimit (Limits and colimits as terminal cones and initial cocones, with existence and uniqueness in their universal properties, Preservation, reflection, and creation of limits and colimits; continuous and cocontinuous functors). Equivalently, a colimit is absolute when every functor preserves it.
Depends on
Used by
Dependency tree · two levels
6 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
- E. Riehl, Category Theory in Context, 2nd ed., Exercise 3.4.vi(iii) and Lemma 5.4.6 (standard reference, not scraped)