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.

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

Revised on November 17, 2009 18:43:31 by Urs Schreiber (131.211.36.96)