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

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