  Co$_2$C nanoparticles (NPs) are amongst transition metal carbides whose
magnetic properties have not been well explored. A recent study by Nirmal Roy
et al. [1] showed that a collection of Co$_2$C NPs exhibit an exchange bias
(EB) effect below T$_{EB}$ = 50 K and also a spin glass (SG) state below
T$_{SG}$ = 5 K. We use magnetic, electrical transport, specific heat, and muon
spin rotation ($\mu$SR) measurements to explore further the magnetic properties
of these NPs. We uncover the onset of Kondo localization at Kondo temperature
T$_K$ (= 40.1 K), near the onset of EB effect. A crossover from the
Kondo-screened scenario to an RKKY interaction-dominated regime is also
observed for T < T$_K$. Specific heat measurements confirm Kondo localization
and heavy fermionic nature in Co$_2$C at low T. At low T, zero field $\mu$SR
spectra reveal a dominant magnetically disordered fraction with slow relaxation
and a smaller fraction with short-range order exhibiting fast relaxation, with
no evidence of long-range magnetic order. We observe an increase in this fast
relaxation rate between T$_{EB}$ and T$_{SG}$, suggesting a slowing down of the
fluctuating local magnetic environment around muons. Transverse field $\mu$SR
spectra show the emergence of a stable, multi-peaked local magnetic field
distribution below T$_{EB}$. Longitudinal field $\mu$SR spectra shows distinct
changes in the dynamics of fluctuations suggesting the presence of a frozen
glassy like state below 6 K. Our results suggest that below T$_{EB}$, Co$_2$C
NPs pellet develops a magnetic interface, separating disordered and short-range
order fractions. The Exchange interaction that sets in below T$_{EB}$ at the
interface couples them and suppresses the fluctuations. With the suppression of
magnetic fluctuations below T$_{EB}$, strong correlation effects in the
electronic state of Co$_2$C lead to Kondo localization.
