The Verdier Quotient In A.Neeman's book and D.Murfet's notes I have been reading about the construction of the Verdier quotient of a triangulated category, $\mathscr{T}$, by some triangulated subcategory $\mathscr{C}$. In both places they require that triangulated subcategories be strict (i.e. closed under taking isomorphisms). Is it possible to remove the strictness assumption and still define the Verdier quotient? I have been studying the proof of existence and I haven't been able to find a place with strictness is required. Thanks!

$\mathscr{T}/\mathscr{C}$ still makes sense if $\mathscr{C}$ is not strict, but it's exactly the same as taking the quotient by the "strictification" of $\mathscr{C}$ (i.e., the subcategory consisting of all objects isomorphic to an object of $\mathscr{C}$), so you don't get anything more general.