Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appearsIn |
Mac Lane's 'Categories for the Working Mathematician'
|
| gptkbp:consistsOf |
morphism η: I → M
morphism μ: M ⊗ M → M object M in a monoidal category |
| gptkbp:definedIn |
monoid object in a monoidal category
|
| gptkbp:dual_concept |
comonoid in category theory
|
| gptkbp:example |
monoid in End(C) is a monad
monoid in Set is a classical monoid |
| gptkbp:field |
gptkb:category_theory
abstract algebra |
| gptkbp:formalized_by |
gptkb:Saunders_Mac_Lane
|
| gptkbp:generalizes |
monoid
|
| gptkbp:has_morphisms |
monoid homomorphisms in the categorical sense
|
| gptkbp:hasProperty |
categorifies the notion of monoid
|
| https://www.w3.org/2000/01/rdf-schema#label |
Monoid in category theory
|
| gptkbp:relatedTo |
gptkb:monoidal_category
|
| gptkbp:satisfies |
associativity axiom
unit axiom |
| gptkbp:used_in |
algebraic structures
theory of monads |
| gptkbp:bfsParent |
gptkb:Monoidal_category
|
| gptkbp:bfsLayer |
7
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