Statements (16)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appearsIn |
Mac Lane's 'Categories for the Working Mathematician'
|
| gptkbp:definedIn |
A functor F: C → D is a left adjoint if there exists a functor G: D → C such that Hom_D(F(c), d) ≅ Hom_C(c, G(d)) naturally in c and d.
|
| gptkbp:example |
Tensor product functor is left adjoint to Hom functor in modules
Free group functor is left adjoint to the forgetful functor from groups to sets |
| gptkbp:field |
Category theory
|
| gptkbp:hasDual |
Right adjoint
|
| https://www.w3.org/2000/01/rdf-schema#label |
Left adjoint
|
| gptkbp:introduced |
gptkb:Daniel_Kan
|
| gptkbp:partner |
Right adjoint
|
| gptkbp:property |
Is a functor
Preserves colimits |
| gptkbp:relatedTo |
gptkb:Adjoint_functor
Right adjoint |
| gptkbp:bfsParent |
gptkb:Adjoint_functor
|
| gptkbp:bfsLayer |
6
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