  Current theories and models attempt to explain star formation globally, from
core scales to giant molecular cloud scales. A multi-scale observational
characterisation of an entire molecular complex is necessary to constrain them.
We investigate star formation in G202.3+2.5, a ~10x3 pc sub-region of the
Monoceros OB1 cloud with a complex morphology harbouring interconnected
filamentary structures. We aim to connect the evolution of cores and filaments
in G202.3+2.5 with the global evolution of the cloud and to identify the
engines of the cloud dynamics. In this first paper, the star formation activity
is evaluated by surveying the distributions of dense cores and protostars, and
their evolutionary state, as characterised using both infrared observations
from the Herschel and WISE telescopes and molecular line observations with the
IRAM 30-m telescope. We find ongoing star formation in the whole cloud, with a
local peak in star formation activity around the centre of G202.3+2.5 where a
chain of massive cores (10-50 Msun) forms a massive ridge (>150 Msun). All
evolutionary stages from starless cores to Class II protostars are found in
G202.3+2.5, including a possibly starless, large column density (8x10^{22}
cm-2), and massive (52 Msun) core. All the core-scale observables examined in
this paper point to an enhanced star formation activity centred on the junction
between the three main branches of the ramified structure of G202.3+2.5. This
suggests that the increased star-formation activity results from the
convergence of these branches. To further investigate the origin of this
enhancement, it is now necessary to extend the analysis to larger scales, in
order to examine the relationship between cores, filaments and their
environment. We address these points through the analysis of the dynamics of
G202.3+2.5 in a joint paper.
