Phrase Hound found 10 phrases and 6 compound words that contain functors. The most common are listed below. Open functors in the live search for definitions, filters, and the full list.
Phrases 10
- adjoint functorsplural of adjoint functor: One 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 …
- faithful functorsplural of faithful functor: A 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.
- forgetful functorsplural of forgetful functor: A functor that forgets or drops some or all of its input's structure or properties before mapping to the output.
- full functorsplural of full functor: A 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.
- group functorsplural of group functor: A group object that is an object in a category of functors; a functor with certain properties that generalise the concept of group.
- identity functorsplural of identity functor: A functor from a category to itself which maps each object of that category to itself and each morphism of that category to itself.
- underlying functorsplural of underlying functor: a forgetful functor
- representable functorsplural of representable functor: A functor from some category to the category of sets (Set) which is naturally isomorphic to a hom functor.
- Yoneda functorsplural of Yoneda functor: A 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 …
- contravariant functorsplural of contravariant functor: A 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).
Compound words 6
- anafunctorsplural of anafunctor: A generalized functor that does not employ the axiom of choice
- profunctorsplural of profunctor: A generalization of a relation in category theory
- endofunctorsplural of endofunctor: A functor that maps a category to itself.
- overfunctorsplural of overfunctor: A morphism of an overcategory.
- pseudofunctorsplural of pseudofunctor: A 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.
- subfunctorsplural of subfunctor: A 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 …