CERN-LHC. Measurement of the cross section for inclusive isolated-photon production in proton-proton collisions at a centre-of-mass energy of 13 TeV with 3.2/fb of data collected in 2015. The photon is required to have a transverse energy above 125 GeV and absolute value of pseudorapity |etaGamma|<2.37, excluding the region 1.37<|etaGamma|<1.56. The photon isolation is ensured by requiring the transverse energy around a cone of radius R=0.4 around the photon to be less than (4.8 + 0.0042 * ETGamma) [GeV]. At particle level it is the sum of transverse energy from all stable particles, except for muons, neutrinos and the photon itself, in a cone of size DeltaR =0.4 around the photon direction after the contribution from the underlying event is subtracted; the same subtraction procedure, based on the jet-area method, used on data is applied at the particle level (see the journal publication for details). At parton level it is the sum of transverse energy from all coloured partons in a cone of size DeltaR =0.4 around the photon direction. Information about the bin-to-bin correlation of the systematic uncertainties. The following uncertainties are to be treated as uncorrelated bin-to-bin: sysPhotonID, sysBackgroundIsolation, sysBackgroundIsolationUpperLimit, sysBackgroundID, sysIsolationMC and sysMCstats. The systematic uncertainty due to the photon energy scale and resolution is partially correlated bin-to-bin and its decomposition into independent sources is given. In order to take into account properly the correlations due to the photon energy scale and resolution, see the information provided below. The systematic uncertainty due to the photon energy scale (GES) and resolution (GER) is decomposed into 78 independent components: starting from the one labelled RESOLUTION_MATERIALCALO__1down,RESOLUTION_MATERIALCALO__1up until the one labelled PH_SCALE_LEAKAGEUNCONV__1down,PH_SCALE_LEAKAGEUNCONV__1up. Each of the 78 independent components has two variations (up and down). The uncertainties due to the up and down variations for each component are not necessarily symmetric and do not necessarily have different signs. Furthermore, the uncertainty for a given variation (up or down) of a given component can change sign bin to bin in Etgamma. As a result, providing the positive and negative uncertainties as such would mean that the correlation between different Etgamma bins and different measurements is lost. To avoid that loss and to provide the information on the correlation the following format is used for the uncertainties of each independent component in the tables 1 to 4: for the upper entry of the uncertainty, the systematic uncertainty of the down variation is given, which can be either positive or negative, and is fully correlated with the upper entries of the other Etgamma bins (for the same component); for the lower entry of the uncertainty, the systematic uncertainty of the up variation is given, which can be either positive or negative, and is fully correlated with the lower entries of the other Etgamma bins (for the same component). For example, for the first component: the upper entry corresponds to the sistematic uncertainty due to RESOLUTION_MATERIALCALO__1down (first part of the label) and the lower entry corresponds to the sistematic uncertainty due to RESOLUTION_MATERIALCALO__1up (second part of the label). Predictions for the differential cross sections (tables 5 to 8) are given at NLO QCD from the program Jetphox using the MMHT2014 NLO PDF set. Four sources of uncertainty are considered and quoted separately for each bin in EtGamma and each region of |etaGamma|: the uncertainty due to terms beyond NLO (TheoryUncertEnvelopeScales), the uncertainty due to that in the PDFs (TheoryUncertPDF), the uncertainty due to that in alphas (TheoryUncertAlphas) and the uncertainty in the non-perturbative corrections (TheoryUncertNonPerturbative). The first one (TheoryUncertEnvelopeScales) was calculated using the envelope of the 14-point scheme of variations of the renormalisation, factorisation and fragmentation scales (variations of one scale up and down by a factor 2 leaving the other two scales unchanged; simultaneous variations of two scales up and down by a factor 2 leaving the other scale unchanged; simultaneous variations of the three scales up and down by a factor 2; variations of two scales in opposite directions are excluded). The second one (TheoryUncertPDF) was calculated using the 50 sets from the MMHT2014 error analysis and applying the asymmetric master formula. The third one (TheoryUncertAlphas) was estimated by repeating the calculations using two additional sets of proton PDFs from the MMHT2014 analysis, for which different values of alphas(mZ) were assumed in the fits, namely alphas(mZ)=0.118 and 0.122; the differences between the nominal calculations and the alphas(mZ)-varied calculations were scaled by a factor 1.5/2. The fourth one (TheoryUncertNonPerturbative) was estimated to be 1%, as described in the journal publication. On the issue of the correlation of the uncertainties between different bins in EtGamma and regions of |etaGamma|: although the correlations could be accounted for some of the sources of uncertainty, for the scale uncertainties, which are the dominant ones, it is far from trivial and subject to debate. Furthermore, since in 2019 NNLO calculations for inclusive photon production have become available, the usefulness of the study of the correlations for NLO predictions is of no relevance.