nLab cell object

Definition

For $(L \dashv R) : C \stackrel{\overset{L}{\leftarrow}}{\underset{R}{\to}} D$ 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)