DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-01

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.

Braided monoidal functor

Definition

Let $(C, c)$ and $(D, c^{'})$ be braided monoidal categories (Braided monoidal category). A braided monoidal functor $F : C \to D$ is a strong monoidal functor (Lax, strong, and strict monoidal functors) with structure isomorphisms

$J_{X, Y} : F (X) \otimes F (Y) \overset{≅}{⟶} F (X \otimes Y), J_{0} : 1_{D} \overset{≅}{⟶} F (1_{C}),$

such that for all objects $X, Y$ ,

$J_{Y, X} \circ c_{F (X), F (Y)}^{'} = F (c_{X, Y}) \circ J_{X, Y} .$

Depends on

Used by

Dependency tree · two levels

7 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

P. Etingof, S. Gelaki, D. Nikshych, and V. Ostrik, Tensor Categories, Definition 8.1.7 (standard reference, not scraped)