4 papers
Cofibrant generation of pure monomorphisms
Michael Lieberman, Leonid Positselski, Jiri Rosicky +1
We show that pure monomorphisms are cofibrantly generated---generated from a set of morphisms by pushouts, transfinite composition, and retracts---in any locally finitely presentab…
Tameness, powerful images, and large cardinals
Will Boney, Michael Lieberman
We provide comprehensive, level-by-level characterizations of large cardinals, in the range from weakly compact to strongly compact, by closure properties of powerful images of acc…
Sizes and filtrations in accessible categories
Michael Lieberman, Jiří Rosický, Sebastien Vasey
Accessible categories admit a purely category-theoretic replacement for cardinality: the internal size. Generalizing results and methods from arXiv:1708.06782, we examine set-theor…
Approximations of superstability in concrete accessible categories
Michael Lieberman, Jiri Rosicky
We generalize the constructions and results of Chapter 10 in Baldwin's "Categoricity" to coherent accessible categories with concrete directed colimits and concrete monomorphisms.…