The phrase "a natural map" is correct and usable in written English.
It is typically used in mathematical contexts, particularly in category theory, to describe a morphism that arises naturally from the structure of the objects involved.
Example: "In this case, we can define a natural map from the homology groups of the space to its cohomology groups."
Alternatives: "a canonical map" or "an induced map".
Hence, we have a natural map (3.2).
Note that there is a natural map (iota _k :_nmathrm{Br}(k) rightarrow _nmathrm{Br}(K _{mathrm{ur}}).
And on the other hand, (alpha _1) induces a natural map (E rightarrow widetilde{E}), so we can form a distinguished triangle Open image in new window and (e^dagger (E)) lies in ({text {Ho}}(mathsf{Ind},mathcal {C}_0)).
Any commutative square (2.4) in (mathcal {C}) with acyclic (Y') induces a natural map (T_dagger (h(f)) rightarrow h(X')), and this map is an isomorphism if and only if (2.4) is homotopy cocartesian.
If we consider M to be a Cartan-Hadamard manifold (either infinite or finite dimensional), then on M there exists a natural map η playing the role of x − y in the R n.
Then for any pair of composable maps (g_1), (g_2) in (Delta I), we have a natural map (c(g_1,g_2):i(g_1)_cdot * i(g_2)_cdot rightarrow i(g_1 circ g_2)_cdot ), and the map (4.2) for the prefibration (widetilde{F}) is the map (alpha (c(g_1,g_2)):g_2^* circ g_1^* rightarrow (g_1 circ g_2)^*).
"We wanted to create a natural mapping as to where the sound is coming from and where you should look".
The two are connected by a natural mapping : Π → L, given by p → [p] = F Jp) where for each p∈Π, Jp = {x∈ X | p(x) ≰ p′ }.
We always have (operatorname{Fix}(mathcal{S} subseteq mathrm{C}(mathcal{S})), and there is a natural mapping (r : mathrm{C}(mathcal{S}) to X) defined by r(x) = lim_{n toinfty} s_{n} (x) for each (xin X).
We use this probabilistic definition because it encompasses a natural mapping between P(x NR ) and the general concept of reputation, i.e., an entity with a high probability of being good (or non-risky) is expected to have high reputation.
There is a natural mapping ρ : Δ G → Π G that assigns to each population its allele frequency spectrum.
