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$t$-structure is a structure imposed on triangulated categories, first introduced in Beilinson, Bernstein, Deligne's "Faisceaux Pervers".
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Monoidality of truncation of spectra
If $X$ is a spectrum, we have a notion of its connective part $X_{\le 0}$ and the corresponding notion of truncation $X_{[i:j]} = X_{\le j}/X_{\le i-1}$, where $X_{\le j}$ is deduced from $X_{\le 0}$ …