A bstract Measurements of the production cross sections of prompt D 0 , D + , D *+ , D s + , Λ c + , and Ξ c + charm hadrons at midrapidity in proton-proton collisions at s = 13 TeV with the ALICE detector are presented. The D-meson cross sections as a function of transverse momentum ( p T ) are provided with improved precision and granularity. The ratios of p T -differential meson production cross sections based on this publication and on measurements at different rapidity and collision energy provide a constraint on gluon parton distribution functions at low values of Bjorken- x (10 − 5 –10 − 4 ). The measurements of Λ c + ( Ξ c + ) baryon production extend the measured p T intervals down to p T = 0(3) GeV /c . These measurements are used to determine the charm-quark fragmentation fractions and the c c ¯ production cross section at midrapidity (| y | < 0 . 5) based on the sum of the cross sections of the weakly-decaying ground-state charm hadrons D 0 , D + , D s + , Λ c + , Ξ c 0 and, for the first time, Ξ c + , and of the strongly-decaying J /ψ mesons. The first measurements of Ξ c + and Σ c 0 , + + fragmentation fractions at midrapidity are also reported. A significantly larger fraction of charm quarks hadronising to baryons is found compared to e + e − and ep collisions. The c c ¯ production cross section at midrapidity is found to be at the upper bound of state-of-the-art perturbative QCD calculations.