On satellites in arbitrary categories
Abstract
Description
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.
3 + 1 pages; translated by Jone Intxaurraga Larranaga and Tim Van der Linden with the help of Alexander Frolkin and Julia Goedecke; with author's remarks
3 + 1 pages; translated by Jone Intxaurraga Larranaga and Tim Van der Linden with the help of Alexander Frolkin and Julia Goedecke; with author's remarks