  Production of the ${^{55-57}}$Co nuclei on ${^{\rm nat}}$Ni in photonuclear
reactions using bremsstrahlung gamma photon irradiation with end-point energy
$E_{\rm{\gamma max}}$ between 35 and 94~MeV has been studied. The experiment
was performed at the electron linear accelerator LUE-40 NSC KIPT using the
methods of $\gamma$ activation and off-line $\gamma$-ray spectroscopy. The
obtained experimental flux-averaged cross-sections
$\langle{\sigma(E_{\rm{\gamma max}})}\rangle$ agree with the data found in
literature. The theoretical flux-averaged cross-sections
$\langle{\sigma(E_{\rm{\gamma max}})}\rangle_{\rm{th}}$ for the production of
${^{55-57}}$Co and ${^{55-57}}$Ni were estimated using the cross-section values
$\sigma(E)$ from the TALYS1.95 code and bremsstrahlung spectra of gamma photons
calculated by GEANT4.9.2. The experimental results for ${^{56,57}}$Co agree
with the cumulative $\langle{\sigma(E_{\rm{\gamma max}})}\rangle_{\rm{th}}$.
However theoretical prediction fails to reproduce the measured cross-sections
for the production of ${^{55}}$Co.
