JournalsrsmupVol. 144pp. 13–25

Unusual spectral categories

  • María José Arroyo Paniagua

    Universidad Autónoma Metropolitana, Iztapalapa, Mexico
  • Alberto Facchini

    Università di Padova, Italy
  • Marino Gran

    Université Catholique de Louvain, Louvain-la-Neuve, Belgium
  • George Janelidze

    University of Cape Town, Rondebosch, South Africa
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Abstract

The paper is devoted to a kind of “very non-abelian” spectral categories. Under strong conditions on a category X\mathcal X, we prove, among other things, that, for a given faithful localization CX\mathcal C \to \mathcal X, we have canonical equivalences Spec(C)X(\mathcal{C})\sim\mathcal{X}\sim(category of injective objects in C)\mathcal{C}), and that C\mathcal{C} has natural injective envelopes.

Cite this article

María José Arroyo Paniagua, Alberto Facchini, Marino Gran, George Janelidze, Unusual spectral categories. Rend. Sem. Mat. Univ. Padova 144 (2020), pp. 13–25

DOI 10.4171/RSMUP/53