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.
The order of the tensor factors in enriched composition is fixed on this page
Remark
Kelly writes the composition map of a -category as
(Enriched category over a monoidal base), and that is the convention fixed for this page. Other authors sometimes reverse the two tensor factors and rewrite every diagram. For a merely monoidal base this is naturally a change from to the reversed monoidal category ; it becomes a convention inside the same base only when a chosen braiding supplies the swap. Silently switching between the two orders without that change destroys the associativity and naturality formulas. Every later formula here keeps Kelly's order.
Depends on
Used by
Nothing in the library uses this result yet.
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
- G. M. Kelly, Basic Concepts of Enriched Category Theory, equation (1.3) (standard reference, not scraped)
- Geoffrey Cruttwell, Normed Spaces and the Change of Base for Enriched Categories, Section 2.2 (standard reference, not scraped)