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Semantic Factorization and Descent
Let be a -category with suitable opcomma objects and
pushouts. We give a direct proof that, provided that the codensity monad of a
morphism exists and is preserved by a suitable morphism, the factorization
given by the lax descent object of the higher cokernel of is up to
isomorphism the same as the semantic factorization of , either one existing
if the other does. The result can be seen as a counterpart account to the
celebrated B\'{e}nabou-Roubaud theorem. This leads in particular to a
monadicity theorem, since it characterizes monadicity via descent. It should be
noted that all the conditions on the codensity monad of trivially hold
whenever has a left adjoint and, hence, in this case, we find monadicity to
be a -dimensional exact condition on , namely, to be an effective
faithful morphism of the -category .Comment: Full revision, new diagrams, 48 page
The spin structure of the proton at low and low in two-dimensional bins from COMPASS
The longitudinal double spin asymmetries and the spin dependent
structure function of the proton were extracted from COMPASS data in
the region of low Bjorken scaling variable and low photon virtuality .
The data were taken in 2007 and 2011 from scattering of polarised muons off
polarised protons, resulting in a sample that is 150 times larger than the one
from the previous experiment SMC that pioneered studies in this kinematic
region.
For the first time, and were evaluated in this region in
two-dimensional bins of kinematic variables: , ,
and . The following kinematic region was investigated: , ~(GeV/)~(GeV/) and
~GeV~GeV. The obtained results were confronted with theoretical
models.Comment: 5 pages, 3 figures, DIS 2016 Conference Proceedings, to appear in the
proceedings of the XXIV International Workshop on Deep-Inelastic Scattering
and Related Subjects, DESY Hamburg, Germany, April 11-15, 201
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