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.

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

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