Homological and cohomological indexing of t-structures

Remark 6.3.2 (Cohomological grading). We index t-structures homologically, matching our convention for chain complexes (Remark 6.1.8). A reader preferring cohomological grading should negate the index throughout, writing \(C^{\geq n} := C_{\leq -n}\) and \(C^{\leq n} := C_{\geq -n}\), and likewise \(\tau ^{\geq n} := \tau _{\leq -n}\) and \(\tau ^{\leq n} := \tau _{\geq -n}\) for the truncation functors introduced below.