Sentence examples for derived section from inspiring English sources
Both the experimentally and numerically derived section capacities were compared with the strength predictions determined from the current European code, the American specification and the Australian/New Zealand standard, allowing the applicability of each codified method to be assessed.
end{aligned} (9.15 Any object (E in {text {Ho}}(mathcal {C})) defines a constant derived section (E_X in {mathcal {D}} X,mathcal {C})).
In particular, for any object (i in I) and derived section (E in {text {DSec}}(I,mathcal {C})), we have (mathsf{ev}_i(R^cdot Phi (E)) cong R^cdot Phi (mathsf{ev}_i(E))).
Moreover, for any derived section s of (mathcal {C}) over I, the adjunction map (rho ^*sigma ^*s rightarrow s) is a pointwise weak equivalence, so that it lies in the image of the fully faithful functor ({text {Ho}}(rho ^*)).
A derived section (E in {text {DSec}}((Delta X)^o,mathcal {C})) of such a stable model prefibration is homotopy special if the section (mathsf{ev}(E)) obtained by applying the evaluation functor (8.5) is special in the sense of Definition 5.10.
For any good model prefibration (mathcal {C}) over a Reedy category I with the matching expansion (rho :M(I) rightarrow I), a derived section (sigma ) of (mathcal {C}) over I is a section (sigma in {text {Sec}}(M(I),rho ^*mathcal {C})) that is homotopy cartesian along all maps f in M(I) vertical with respect to (rho ).
Another corollary of Proposition 8.4 is extended functoriality for the categories of derived sections.
As it turns out, if restrict our attention to homotopy special derived sections, then we do not even need to consider the simplicial expansion (Delta I).
The full subcategory in ({text {Sec}}(M(I),rho ^*mathcal {C})) spanned by derived sections is denoted by ({text {Sec}}_{rho }(M(I),rho ^*mathcal {C})).
In order to apply Proposition 8.4, it is useful to obtain a version of the isomorphisms (7.7) and (7.8) valid for derived sections.
We can also combine this construction with Example 8.12 to apply it to derived sections over the category (I times [1]^o).
