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Corpus ID: 211146364

Detecting isomorphisms in the homotopy category.

@article{Arlin2019DetectingII,
title={Detecting isomorphisms in the homotopy category.},
author={Kevin Arlin and J. Daniel Christensen},
journal={arXiv: Algebraic Topology},
year={2019}
}

We show that the homotopy category of unpointed spaces admits no set of objects jointly reflecting isomorphisms by giving an explicit counterexample involving large symmetric groups. We also show that, in contrast, the spheres jointly reflect equivalences in the homotopy 2-category of spaces. The non-existence of such a set in the homotopy category was originally claimed by Heller, but his argument relied on the statement that for every set of spaces, long enough transfinite sequential diagrams… Expand

We prove general adjoint functor theorems for weakly (co)complete n-categories. This class of n-categories includes the homotopy n-categories of (co)complete ∞-categories – in particular, these… Expand

CW-complexes generalities on homotopy classes of mappings homotopy groups homotopy theory of CW-complexes homotopy with local coefficients homology of fibre spaces elementary theory the homology… Expand

We prove that the 2-category of spaces admits a strong generator made up of the tori. In other words, Whitehead's theorem holds for the 2-category of (not necessarily connected, not pointed) spaces.