nLab
deformation retract for the enrichment

Definition

A deformation retract for the enrichment of a category $C$ enriched over a closed monoidal homotopical category $V$ is a deformation retract of a homotopical category for the two-variable adjunction

(power, copower, internal hom) : $V\times C\to C$

satisfying a bunch of extra conditions.

References

This is definition 16.1, p. 46 in Shulman: Homotopy limits and colimits and enriched homotopy theory