  We study the Kondo effect for a $\Sigma_{c}$ ($\Sigma_{c}^{\ast}$) baryon in
nuclear matter. In terms of the spin and isospin
($\mathrm{SU}(2)_{\mathrm{spin}} \times \mathrm{SU}(2)_{\mathrm{isospin}}$)
symmetry, the heavy-quark spin symmetry and the S-wave interaction, we provide
the general form of the Lagrangian for a $\Sigma_{c}$ ($\Sigma_{c}^{\ast}$)
baryon and a nucleon. We analyze the renormalization equation at the one-loop
level, and find that the coexistence of spin exchange and isospin exchange
magnifies the Kondo effect in comparison with the case where the spin-exchange
interaction and the isospin-exchange interaction exist separately. We
demonstrate that the solution exists for the ideal sets of the coupling
constants, including the $\mathrm{SU}(4)$ symmetry as an extension of the
$\mathrm{SU}(2)_{\mathrm{spin}} \times \mathrm{SU}(2)_{\mathrm{isospin}}$
symmetry. We also conduct a similar analysis for the Kondo effect of a
$\bar{D}$ ($\bar{D}^{\ast}$) meson in nuclear matter. On the basis of the
obtained result, we conjecture that there could exist a "mapping" from the
heavy meson (baryon) in vacuum onto the heavy baryon (meson) in nuclear matter.
