Say that a derived section of (widetilde{mathcal {C}}) on either of these two categories is homotopy special if it is homotopy cartesian along all special maps, and let ({text {DSec}}_+ subset {text {DSec}}) stand for the full subcategory spanned by homotopy special sections.
Another corollary of Proposition 8.4 is extended functoriality for the categories of derived sections.
In the assumptions above, the essential image of the fully faithful functor (gamma _*:{text {DSec}}(I',gamma ^*mathcal {C}) rightarrow {text {DSec}}(I,mathcal {C})) consists of derived sections that are homotopy cartesian along (a(i):i rightarrow gamma (gamma _dagger (i))) for all (i in I).
Then we have the full embedding begin{aligned} gamma ^o_!:{text {DSec}} overline{Delta }^o,widetilde{mathcal {C}}) rightarrow {text {DSec}}((Delta P ^o,R(mathcal {C},Phi )), end{aligned}and to prove the claim, it suffices to show that its essential image consists of derived sections that are homotopy cartesian along all the maps in the class L in ((Delta P ^o).
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 ^*)).
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 ).
The questionnaire was derived from sections of several social behavior and attraction questionnaires that included questions regarding physical activity (International Physical Activity Questionnaire; "IPAQ", 2002), sleep patterns (Karolinska Sleep Questionnaire) [ 17, 18], and interpersonal relations (Interpersonal Attraction Scales) [ 19, 20].
He spent six months designing a building with sail-like roofs, their geometry, he said, derived from the sections of an orange.
Cytoarchitectonic maps of areas 44 and 45 were derived from histologic sections of 10 postmortem brains.
Eight different microscopic fields derived from different sections of three different tumors were photographed.
