Phrase Hound found 12 phrases and 9 compound words that contain functor. The most common are listed below. Open functor in the live search for definitions, filters, and the full list.
Phrases 12
- contravariant functorA functor which maps a morphism f:X → Y to a morphism F(f):F(Y) → F(X), such that if h=g∘f, then F(h)=F(f)∘F(g).
- group functorA group object that is an object in a category of functors; a functor with certain properties that generalise the concept of group.
- functor categoryA category whose objects are functors (from some fixed given domain category to some fixed given codomain category) and whose morphisms are natural transformations.
- forgetful functorA functor that forgets or drops some or all of its input's structure or properties before mapping to the output.
- underlying functora forgetful functor
- faithful functorA functor which maps morphisms from its source to its target category in such a way that the restriction of that mapping to any source hom-set is injective into the corresponding target hom-set.
- full functorA functor which maps morphisms from its source to its target category in such a way that the restriction of that mapping to any source hom-set is surjective into the corresponding target hom-set.
- identity functorA functor from a category to itself which maps each object of that category to itself and each morphism of that category to itself.
- adjoint functorOne of a pair of functors such that the domain and codomain of one of them are identical to the codomain and domain of the other one, respectively, and such that there is a pair of natural transformations which turns the pair of functors …
- representable functorA functor from some category to the category of sets (Set) which is naturally isomorphic to a hom functor.
- Yoneda functorA functor from a given category to the category of functors from that given category to Set (the category of sets) which maps any object of the given category to a hom functor represented by that object and any morphism to a natural …
- functor categoriesplural of functor category: A category whose objects are functors (from some fixed given domain category to some fixed given codomain category) and whose morphisms are natural transformations.
Compound words 9
- functorialAble to be described as a functor.
- endofunctorA functor that maps a category to itself.
- bifunctorA functor whose domain is a product of categories.
- subfunctorA functor such that all of the objects it maps are mapped by the parent functor, and for any arrow it maps the parent functor includes the same mapping (although it may also map arrows from the same domain to additional images outside the …
- anafunctorA generalized functor that does not employ the axiom of choice
- overfunctorA morphism of an overcategory.
- profunctorA generalization of a relation in category theory
- pseudofunctorA mapping between categories that is just like a functor except that f(x∘y)=f(x)∘f(y) and f(1)=1 do not hold as exact equalities but only up to coherent isomorphisms.
- semifunctorA generalization of a functor.