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On the Recollements of Functor Categories

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Abstract

This paper is devoted to the study of recollements of functor categories in different levels. In the first part of the paper, we start with a small category \(\mathcal {S}\) and a maximal object s of \(\mathcal {S}\) and construct a recollement of \(\text {Mod-}\mathcal {S}\) in terms of \(\text {Mod-End}_{\mathcal {S}}(s)\) and \(\text {Mod-}(\mathcal {S}\setminus \{s\})\) in four different levels. In case \(\mathcal {S}\) is a finite directed category, by iterating this argument, we get chains of recollements having some interesting applications. In the second part, we start with a recollement of rings and construct a recollement of their path rings, with respect to a finite quiver. Third part of the paper presents some applications, including recollements of triangular matrix rings, an example of a recollement in Gorenstein derived level and recollements of derived categories of N-complexes.

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Authors and Affiliations

  1. Department of Mathematics, University of Isfahan, P.O. Box: 81746-73441, Isfahan, Iran

    Javad Asadollahi

  2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran

    Javad Asadollahi, Rasool Hafezi & Razieh Vahed

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  1. Javad Asadollahi
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  2. Rasool Hafezi
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  3. Razieh Vahed
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Correspondence to Javad Asadollahi.

Additional information

This research was in part supported by a grant from IPM (No: 92130216, 93130063).

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Asadollahi, J., Hafezi, R. & Vahed, R. On the Recollements of Functor Categories. Appl Categor Struct 24, 331–371 (2016). https://doi.org/10.1007/s10485-015-9399-6

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