# Name for functors preserving and reflecting weak equivalences?

Is there an established name for functors between Quillen model categories (or actually any homotopical category) preserving and reflecting weak equivalences ?

This is kind of the homotopical version of conservative functors (i.e. preserving (of course) and reflecting isomorphisms), so I'm tempted to call them homotopically conservative or something. But maybe there already is a name out there ?

• I like the name homotopically conservative! – Charles Sep 8 '18 at 21:06