On satellites in arbitrary categories

Details On satellites in arbitrary categories On satellites in arbitrary categories

2008-09-09

arxiv.org/abs/0809.1504v1

G. Z. Janelidze, On satellites in arbitrary categories, Bull. Georgian Acad. Sci. 82 (1976), no. 3, 529-532, in Russian

Mathematics

Algebraic Topology

3 + 1 pages; translated by Jone Intxaurraga Larranaga and Tim Van der Linden with the help of Alexander Frolkin and Julia Goed

Scientific paper

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.

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