Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
Category theory concept |
| gptkbp:definedIn |
Category C with a bifunctor ⊗: C × C → C
Natural isomorphisms α, λ, ρ, and σ Unit object I |
| gptkbp:example |
gptkb:Category_of_sets_with_cartesian_product
Category of vector spaces with tensor product Category of abelian groups with tensor product |
| gptkbp:hasProperty |
gptkb:Symmetry
gptkb:Bifunctor Associativity Coherence conditions Unit object Natural isomorphism |
| https://www.w3.org/2000/01/rdf-schema#label |
Symmetric monoidal category
|
| gptkbp:isomorphicTo |
Associator α
Left unitor λ Right unitor ρ Symmetry isomorphism σ_{A,B}: A⊗B → B⊗A |
| gptkbp:namedFor |
Category theory
|
| gptkbp:referencedIn |
Saunders Mac Lane, Categories for the Working Mathematician
|
| gptkbp:relatedTo |
gptkb:Monoidal_functor
gptkb:Braided_monoidal_category Closed monoidal category |
| gptkbp:satisfies |
Coherence conditions (Mac Lane's coherence theorem)
|
| gptkbp:subclassOf |
gptkb:Monoidal_category
|
| gptkbp:usedIn |
gptkb:algebra
gptkb:Topology Mathematical physics Quantum computing |
| gptkbp:bfsParent |
gptkb:Symmetric_monoidal_functor
|
| gptkbp:bfsLayer |
6
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