Completeness of standard t-structures

Example 6.3.29. Let \(\Aa \) be an abelian category. The standard t-structure on \(\D (\Aa )\) is left and right separated: an infinitely connective or infinitely coconnective complex has trivial homology and is therefore zero. If \(\Aa \) has exact countable products, then the t-structure is left complete; if it has exact countable coproducts, then it is right complete. Indeed, the countable version of the construction underlying Corollary 6.1.29 supplies the required (co)products in \(\D (\Aa )\), and the criterion below applies.