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.