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.

Co-Eilenberg–Moore category of a comonad

Definition

For a comonad $G$ on $C$ , the co-Eilenberg–Moore category $C_{G}$ has $G$ -coalgebras as objects and coalgebra homomorphisms as morphisms. Its identities and composition are those of $C$ , whose closure is supplied by Coalgebra homomorphisms are closed under identities and composition. The forgetful functor $U^{G} : C_{G} \to C$ sends a coalgebra and a coalgebra homomorphism to their underlying object and arrow.

Depends on

Coalgebra homomorphisms are closed under identities and composition

Used by

The cofree–forgetful co-Eilenberg–Moore adjunction induces the given comonad Theorem

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., Exercise 5.2.iii (standard reference, not scraped)