nLab closed monoidal deformation retract

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

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

such that a bunch of conditions are satisfied.


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


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

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