On satellites in arbitrary categories
Algebraic Topology
2008-09-10 v1 Category Theory
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.
Cite
@article{arxiv.0809.1504,
title = {On satellites in arbitrary categories},
author = {George Janelidze},
journal= {arXiv preprint arXiv:0809.1504},
year = {2008}
}
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