Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Functor
gptkb:mathematical_concept |
| gptkbp:appearsIn |
Category theory textbooks
|
| gptkbp:contrastsWith |
gptkb:Fully_faithful_functor
Full functor |
| gptkbp:definedIn |
A functor that is injective on hom-sets
|
| gptkbp:example |
The inclusion functor from a subcategory
The forgetful functor from the category of groups to sets |
| gptkbp:field |
gptkb:Mathematics
Category theory |
| gptkbp:hasProperty |
Preserves distinct morphisms
|
| gptkbp:hasWikipediaPage |
https://en.wikipedia.org/wiki/Faithful_functor
|
| https://www.w3.org/2000/01/rdf-schema#label |
Faithful functor
|
| gptkbp:opposedBy |
gptkb:Unfaithful_functor
|
| gptkbp:property |
For any two objects X, Y, the map Hom(X,Y) → Hom(F(X),F(Y)) is injective
|
| gptkbp:relatedConcept |
gptkb:Forgetful_functor
|
| gptkbp:used_in |
gptkb:algebra
gptkb:logic gptkb:Topology gptkb:Representation_theory |
| gptkbp:bfsParent |
gptkb:Functor
|
| gptkbp:bfsLayer |
5
|