DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (deepseek-v4-pro + claude-opus-5[1m])audited 2026-08-24

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.

Split coequalizer diagrams

Definition

A split coequalizer diagram consists of morphisms

$x \begin{array}{c} \overset{f}{\to} \\ \to_{g}^{} \end{array} y \overset{h}{\to} z, t : y \to x, s : z \to y$

such that

$h f = h g, h s = 1_{z}, g t = 1_{y}, f t = s h .$

Thus a split coequalizer diagram has maps $f, g : x ⇉ y$ , $h : y \to z$ , $t : y \to x$ , and $s : z \to y$ satisfying $h f = h g$ , $h s = 1_{z}$ , $g t = 1_{y}$ , and $f t = s h$ . The morphism $h$ is called a split coequalizer of $f$ and $g$ (Equalizers and coequalizers as limits and colimits of a parallel pair).

Depends on

Equalizers and coequalizers as limits and colimits of a parallel pair

Used by

Dependency tree · two levels

2 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., Definition 5.4.4 (standard reference, not scraped)
S. Mac Lane, Categories for the Working Mathematician, 2nd ed., Section VI.6 (standard reference, not scraped)