Abstract

Let A, B and C be artin algebras such that there is a recollement of D(ModA) relative to D(ModB) and D(ModC). We compare the algebras A, B and C with respect to syzygy-finite properties and Igusa-Todorov properties under suitable conditions and consider relevant results in the recollements of the bounded derived categories. Further, we characterize when the functor j⁎ (resp., i⁎, i!) in a recollement (Db(modB), Db(modA), Db(modC), i⁎, i⁎, i!, j!, j⁎, j⁎) is an eventually homological isomorphism.

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