nLab closed monoidal deformation retract

A closed monoidal deformation retract on a closed (symmetric) monoidal homotopical category $(V, \otimes, [-,-])$ is a deformation retract of a homotopical category $(V_Q, V_Q, V_R)$ for the two-variable adjunction

$$(\otimes , [-,-], [-,-]) : V \times V \to V$$

such that a bunch of conditions are satisfied.

Remarks

Such closed monoidal deformation retracts are used to characterize closed monoidal homotopical categories.

References

This appears as definition 15.3, p. 44 in Shulman: Homotopy limits and colimits in enriched homotopy theory