3 papers
math.AT2019
Detecting isomorphisms in the homotopy category
Kevin Arlin, J. Daniel Christensen
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 group…
math.AT2018
On Whitehead's theorem beyond pointed connected spaces
Kevin Arlin
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, no…
math.CT2016
On the -categorical Whitehead theorem and the embedding of quasicategories in prederivators
Kevin Arlin
We show that small quasicategories embed, both simplicially and 2-categorically, into prederivators defined on arbitrary small categories, so that in some senses prederivators can…