nLab
cell object

Definition

For $(L⊣R):C\stackrel{\stackrel{L}{\leftarrow }}{\underset{R}{\to }}D$ a pair of adjoint functors between model categories $C$ and $D$, an object $X\in C$ is an $L$-cell object if it is connected to the initial object by a (possibly transfinite) composition of pushouts of morphisms of the form $L(f)$.

References

Definition 3.2 in

• Stefan Schwede, Brooke Shipley, Equivalences of monoidal model categories , Algebr. Geom. Topol. 3 (2003), 287–334 (arXiv)