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searching for Commutative diagram 34 found (174 total)

Proper morphism (2,834 words) [view diff] exact match in snippet view article find links to article

{\displaystyle {\text{Spec}}(\mathbb {C} )} , this is given by the commutative diagram Δ ∗ → X ↓ ↓ Δ → Y {\displaystyle {\begin{matrix}\Delta ^{*}&\to &X\\\downarrow

Double complex (568 words) [view diff] exact match in snippet view article find links to article

{\displaystyle d_{h}\circ d_{v}=d_{v}\circ d_{h}} Hence a double complex is a commutative diagram of the form ⋮ ⋮ ↑ ↑ ⋯ → C p , q + 1 → C p + 1 , q + 1 → ⋯ ↑ ↑ ⋯ →

Michael J. Hopkins (1,012 words) [view diff] exact match in snippet view article find links to article

work is about refining a homotopy commutative diagram of ring spectra up to homotopy to a strictly commutative diagram of highly structured ring spectra

Cofibration (1,643 words) [view diff] exact match in snippet view article find links to article

0)&=f'(x)\end{aligned}}} We can encode this condition in the following commutative diagram where S I {\displaystyle S^{I}} is the path space of S {\displaystyle

Modification (mathematics) (192 words) [view diff] exact match in snippet view article

}}\rightarrow {\boldsymbol {\mathbf {\beta _{f}} }}} . The following commutative diagram shows an example of a modification and its inner workings. Mac Lane

Adams resolution (1,407 words) [view diff] exact match in snippet view article find links to article

X_{0}=X} and K 0 = K {\displaystyle K_{0}=K} . Then, we can form a commutative diagram X 0 ← X 1 ↓ K 0 {\displaystyle {\begin{matrix}X_{0}&\leftarrow &X_{1}\\\downarrow

List of lemmas (525 words) [view diff] exact match in snippet view article find links to article

A commutative diagram that illustrates the five lemma

Hopf algebra of permutations (381 words) [view diff] exact match in snippet view article find links to article

(denoted Sym, QSym, and NSym respectively), as depicted the following commutative diagram. The duality between QSym and NSym is shown in the main diagonal

Dold–Kan correspondence (985 words) [view diff] exact match in snippet view article find links to article

{\displaystyle d_{i}(NA_{n})=0} . Now, composing these differentials gives a commutative diagram N A n → ( − 1 ) n d n N A n − 1 → ( − 1 ) n − 1 d n − 1 N A n − 2

Quotient stack (1,234 words) [view diff] exact match in snippet view article find links to article

′ → T ′ {\displaystyle P'\to T'} is a bundle map (i.e., forms a commutative diagram) that is compatible with the equivariant maps P → X {\displaystyle

Quasi-fibration (1,152 words) [view diff] exact match in snippet view article find links to article

constant path. By definition, p factors through Ep such that one gets a commutative diagram Applying πn yields the alternative definition. Every Serre fibration

Kan fibration (3,273 words) [view diff] exact match in snippet view article find links to article

function complex in the category of simplicial sets) induced from the commutative diagram Hom ( L , X ) → p ∗ Hom ( L , Y ) i ∗ ↓ ↓ i ∗ Hom ( K , X ) → p ∗

Category of topological vector spaces (783 words) [view diff] exact match in snippet view article find links to article

adjoint too (and the corresponding left adjoints fit in an analogue commutative diagram). This left adjoint defines "free topological vector spaces". Explicitly

Atiyah–Singer index theorem (7,553 words) [view diff] exact match in snippet view article find links to article

f:X\to Y} of compact stably almost complex manifolds, then there is a commutative diagram K ( X ) → Td ( X ) ⋅ ch H ( X ; Q ) f ∗ ↓ ↓ f ∗ K ( Y ) → Td ( Y

Dual Steenrod algebra (818 words) [view diff] exact match in snippet view article find links to article

comultiplication. We can summarize this duality through dualizing a commutative diagram of the Steenrod's Hopf algebra structure: A p ∗ → ψ ∗ A p ∗ ⊗ A p

Iitaka dimension (1,128 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \varphi :M\longrightarrow W} , m-pluricanonical map brings the commutative diagram depicted in the left figure, which means that Φ m K ( M ) = Φ m K

World manifold (1,526 words) [view diff] exact match in snippet view article find links to article

compact subgroup S O ( 3 ) {\displaystyle SO(3)} . Thus, there is the commutative diagram G L ( 4 , R ) → S O ( 4 ) {\displaystyle GL(4,\mathbb {R} )\to SO(4)}

Principalization (algebra) (9,028 words) [view diff] exact match in snippet view article

~ G , H {\displaystyle {\tilde {T}}_{G,H}} are connected by the commutative diagram in Figure 1 via the isomorphisms induced by the Artin maps, that

Polynomial hierarchy (2,826 words) [view diff] exact match in snippet view article find links to article

Commutative diagram equivalent to the polynomial time hierarchy. The arrows denote inclusion.

Isbell duality (1,478 words) [view diff] exact match in snippet view article find links to article

note:In order for this commutative diagram to hold, it is required that A {\displaystyle {\mathcal {A}}} is small and E is co-complete.

Higher local field (1,381 words) [view diff] exact match in snippet view article find links to article

field level, using the border map of Milnor K-theory to create a commutative diagram involving the reciprocity map on the level of the field and the residue

Dold–Thom theorem (1,935 words) [view diff] exact match in snippet view article find links to article

Hurewicz homomorphism h: πn(X) → H̃n(X), meaning that one has a commutative diagram where i* is the map induced by the inclusion i: X = SP1(X) → SP(X)

Hopf algebroid (2,150 words) [view diff] exact match in snippet view article find links to article

either side gives the identity morphism. This can be encoded by the commutative diagram below where the dashed arrows represent the existence of these two

Deformation (mathematics) (4,021 words) [view diff] exact match in snippet view article

the plane curve singularity given by the opposite diagram of the commutative diagram of analytic algebras C { x , y } ( y 2 − x n ) ← C { x , y , s }

Spin structure (4,373 words) [view diff] exact match in snippet view article find links to article

exactly a double covering of P E {\displaystyle P_{E}} fitting into a commutative diagram Spin ⁡ ( n ) → P ~ E → M ↓ ↓ ↓ SO ⁡ ( n ) → P E → M {\displaystyle

Flat morphism (3,522 words) [view diff] exact match in snippet view article find links to article

f : X → S {\displaystyle f\colon X\to S} is flat, there exists a commutative diagram X → Hilb S ↓ ↓ S → S {\displaystyle {\begin{matrix}X&\to &\operatorname

Quot scheme (2,273 words) [view diff] exact match in snippet view article find links to article

{E}}_{T}&{\xrightarrow {q'}}&{\mathcal {F}}'\end{matrix}}} is a commutative diagram for E T → i d E T {\displaystyle {\mathcal {E}}_{T}{\xrightarrow

Azumaya algebra (3,208 words) [view diff] exact match in snippet view article find links to article

0} and from Local class field theory, there is the following commutative diagram: H Gal 2 ( Gal ( E 2 / F ) , E 1 × ) → H Gal 2 ( Gal ( E 1 / F )

Groupoid (6,214 words) [view diff] exact match in snippet view article find links to article

y ′ ) {\displaystyle (x,\phi ,y),(x',\phi ',y')} ⁠, there is a commutative diagram in Z {\displaystyle Z} of ⁠ f ( α ) : f ( x ) → f ( x ′ ) {\displaystyle

Determinant (13,819 words) [view diff] exact match in snippet view article find links to article

f(\det((a_{i,j})))=\det((f(a_{i,j})))} holds. In other words, the displayed commutative diagram commutes. For example, the determinant of the complex conjugate of

Kodaira–Spencer map (3,810 words) [view diff] exact match in snippet view article find links to article

}(z_{\beta })=z_{\alpha }} Recall that a deformation is given by a commutative diagram X → X ↓ ↓ Spec ( C ) → Spec ( C [ ε ] ) {\displaystyle {\begin{matrix}X&\to

Cotangent complex (4,731 words) [view diff] exact match in snippet view article find links to article

We can reformulate it as considering the set of extensions of the commutative diagram 0 → G → O X ′ → O X → 0 ↑ ↑ ↑ 0 → I → O S ′ → O S → 0 {\displaystyle

Complex torus (5,905 words) [view diff] exact match in snippet view article find links to article

trivial kernel. These facts can all be summarized in the following commutative diagram 1 → Hom ( Λ , U ( 1 ) ) → P ( Λ ) → N S ( X ) → 0 ↓ ↓ ↓ 1 → Pic 0

Glossary of power electronics (6,500 words) [view diff] case mismatch in snippet view article find links to article

1.A. — A Commutative Diagram.