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arXiv:0809.1504

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Title: On satellites in arbitrary categories
Authors: George Janelidze
Categories: math.AT Algebraic Topology (math.CT Category Theory)
Comments: 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
MSC: 18E25; 18G10
Journal reference: G. Z. Janelidze, On satellites in arbitrary categories, Bull. Georgian Acad. Sci. 82 (1976), no. 3, 529-532, in Russian

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.

Owner: Tim Van der Linden
Version 1: Tue, 9 Sep 2008 11:00:45 GMT

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