In mathematics, a canonical map, also called a natural map, is a map or morphism between objects that arises naturally from the definition or the construction...

In mathematics, the canonical bundle of a non-singular algebraic variety V {\displaystyle V} of dimension n {\displaystyle n} over a field is the line...

classes as sets. In this case, the canonical surjection that maps an element to its class is replaced by the function that maps an element to the representative...

this canonical map Cong : X ′ → X ¯ ′ {\displaystyle \operatorname {Cong} :X^{\prime }\to {\overline {X}}^{\prime }} reduces down to the identity map. Inner...

{\displaystyle K} is a map ϕ : V × V → K {\displaystyle \phi :V\times V\rightarrow K} . The partial evaluation provides a canonical map to the dual vector...

with the finest topology that makes continuous the canonical projection map (the function that maps points to their equivalence classes). In other words...

it with the canonical norm (defined in the same way as the canonical norm on the continuous dual space of H). A sesquilinear form is a map B : H × H →...

structure to itself. An isomorphism between two structures is a canonical isomorphism (a canonical map that is an isomorphism) if there is only one isomorphism...

system at any given point in time Canonical map, a morphism that is uniquely defined by its main property Canonical polyhedron, a polyhedron whose edges...

{\displaystyle S_{0}} . Then for each p ≥ 0 {\displaystyle p\geq 0} the canonical (continuous) map: ( R p f ∗ F ) ∧ → lim ← k ⁡ R p f ∗ F k {\displaystyle (R^{p}f_{*}{\mathcal...

{P} (H^{0}(X,K_{X}^{d}))=\mathbf {P} ^{P_{d}-1},} called the d-canonical map. The canonical ring R(KX) of a variety X is the graded ring R ( K X ) := ⨁ d...

dimension of the variety. The canonical ring and therefore likewise the Kodaira dimension is a birational invariant: Any birational map between smooth compact...

that the canonical map is an affine transformation. It is also sometimes called an oriented affine n-simplex to emphasize that the canonical map may be...

Canonical Ltd. is a privately-held computer software company based in London, England. It was founded and funded by South African entrepreneur Mark Shuttleworth...

class under a given equivalence relation is known as the canonical projection. The evaluation map sends a function f to the value f(x) for a fixed x. The...

through canonical maps is not possible, but Bott–Chern cohomology canonically maps into both. A similiar cohomology theory, into which both map and which...

space is a locally convex topological vector space for which the canonical evaluation map from X {\displaystyle X} into its bidual (which is the strong dual...

and this canonical map Cong : H ∗ → H ¯ ∗ {\displaystyle \operatorname {Cong} :H^{*}\to {\overline {H}}^{*}} reduces down to the identity map. Two vectors...

) For v in V, the map f → f ( v ) {\displaystyle f\to f(\mathbf {v} )} is a linear form on V*. This defines the canonical linear map from V into (V*)*...

reducers that query them. The canonical MapReduce example counts the appearance of each word in a set of documents: function map(String name, String document):...

inclusion map Spec ⁡ ( R / I ) → Spec ⁡ ( R ) {\displaystyle \operatorname {Spec} (R/I)\to \operatorname {Spec} (R)} induced by the canonical map R → R /...

Monastyrsky (2001) canonical A reference to a standard or choice-free presentation of some mathematical object (e.g., canonical map, canonical form, or canonical ordering)...

every quasi-coherent sheaf F {\displaystyle {\mathcal {F}}} on X, the canonical map ⨁ n ≥ 0 Γ ( X , F ⊗ O X L ⊗ n ) ⊗ Z L ⊗ − n → F {\displaystyle \bigoplus...

two sheaves induces maps between their stalks. Finally, there is a canonical map of sheaves F → Gode ⁡ ( F ) {\displaystyle F\to \operatorname {Gode}...

we set φ P : R → R P {\displaystyle \varphi _{P}:R\to R_{P}} is the canonical map from a ring to its localization, and the intersection runs through all...

of another topological space X, equipped with a topology so that the canonical map i : x ↦ { x } ¯ , {\displaystyle i:x\mapsto {\overline {\{x\}}},} is...

metric determines a canonical affine connection, and the exponential map of the (pseudo) Riemannian manifold is given by the exponential map of this connection...

framing the previous year. The technique was further developed within Canonical UK between 2008 and 2010[independent source needed] and components of...

the graph of the hyperelliptic involution to the canonical divisor class. Moreover, the canonical map C → | K C | ∗ {\displaystyle C\to |K_{C}|^{*}} is...

as an algebraic space (for example, by the Keel–Mori theorem). The canonical map [ X / G ] → X / G {\displaystyle [X/G]\to X/G} , that sends a bundle...