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searching for Forgetful functor 10 found (91 total)

Amnestic functor (150 words) [view diff] exact match in snippet view article find links to article

an identity. An example of a functor which is not amnestic is the forgetful functor Metc→Top from the category of metric spaces with continuous functions

Moduli stack of vector bundles (324 words) [view diff] exact match in snippet view article find links to article

Vect n → C {\displaystyle p:\operatorname {Vect} _{n}\to C} be the forgetful functor. Via p, Vect n {\displaystyle \operatorname {Vect} _{n}} is a prestack

Density theorem (category theory) (798 words) [view diff] exact match in snippet view article

( F u ) ( y ) = x . {\displaystyle (Fu)(y)=x.} It comes with the forgetful functor p : I → C {\displaystyle p:I\to C} . Then F is the colimit of the

Double groupoid (1,536 words) [view diff] exact match in snippet view article find links to article

9ex]&h'k'&\end{pmatrix}}} This construction is the right adjoint to the forgetful functor which takes the double groupoid as above, to the pair of groupoids

Prestack (4,266 words) [view diff] exact match in snippet view article find links to article

y X {\displaystyle y':U\to V{\overset {y}{\to }}X} . Through the forgetful functor to C, this category F is fibered in groupoids and is known as an action

Category of elements (2,842 words) [view diff] exact match in snippet view article find links to article

X as well. Let π : C F → C {\displaystyle \pi :C_{F}\to C} be the forgetful functor and the category associated to a contravariant pseudofunctor F {\displaystyle

Complex affine space (2,538 words) [view diff] exact match in snippet view article find links to article

natural linear structure, and so inherits an affine structure under the forgetful functor. Another example is the set of solutions of a second-order inhomogeneous

Stack (mathematics) (5,113 words) [view diff] exact match in snippet view article

such that h ( ϕ ) ( y ) = x {\displaystyle h(\phi )(y)=x} . Via the forgetful functor p : H → ( S c h / S ) {\displaystyle p:H\to (Sch/S)} , the category

Tensor product of modules (8,471 words) [view diff] exact match in snippet view article find links to article

functor − ⊗ R S {\displaystyle -\otimes _{R}S} is a left adjoint to the forgetful functor ⁠ Res R {\displaystyle \operatorname {Res} _{R}} ⁠, which restricts

Faithfully flat descent (2,626 words) [view diff] exact match in snippet view article find links to article

subset U and a quasi-coherent sheaf on it and p {\displaystyle p} the forgetful functor ( U , F ) ↦ U {\displaystyle (U,F)\mapsto U} . There is a succinct