On satellites in arbitrary categories

zbMATH Open0335.18003arXiv0809.1504MaRDI QIDQ4102030

George Janelidze

Publication date: 1976

Abstract: We generalize the definition of satellites with respect to presheaves (and copresheaves) with trace in the sense of Inassaridze; a presheaf with trace is replaced by a graph with a pair of diagrams defined on it. We show that the right satellite functor is left adjoint to the left satellite functor, and that a functor having a right (left) adjoint preserves right (left) satellites. In particular cases the construction of satellites is given.

Full work available at URL: https://arxiv.org/abs/0809.1504

Mathematics Subject Classification ID

Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) (18A40) Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) (18F20)

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