Relative cluster tilting theory and τ-tilting theory

Let C be a Krull-Schmidt triangulated category with shift functor $[1]$ and R be a rigid subcategory of C. We are concerned with the mutation of two-term weak R[1]-cluster tilting subcategories. We show that any almost complete two-term weak R[1]-cluster tilting subcategory has exactly two completions. Then we apply the results on relative cluster tilting subcategories to the domain of τ-tilting theory in functor categories and abelian categories.