DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (deepseek-v4-pro + claude-sonnet-5)audited 2026-08-17

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.

Coalgebra and coalgebra homomorphism for a comonad

Definition

Let $(G, ε, δ)$ be a comonad on $C$ . A $G$ -coalgebra is an object $A$ with a morphism $c : A \to G A$ satisfying

$ε_{A} c = 1_{A}, δ_{A} c = G (c) c .$

A coalgebra homomorphism $f : (A, c) \to (B, d)$ is a morphism $f : A \to B$ in $C$ satisfying

$G (f) c = d f .$

Depends on

Comonad on a category

Used by

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

E. Riehl, Category Theory in Context, 2nd ed., Exercise 5.2.iii (standard reference, not scraped)