Homology, Homotopy and Applications

Volume 16 (2014)

Number 2

Coalgebraic models for combinatorial model categories

Pages: 171 – 184

DOI: http://dx.doi.org/10.4310/HHA.2014.v16.n2.a9


Michael Ching (Department of Mathematics and Statistics, Amherst College, Amherst, Massachusetts, U.S.A.)

Emily Riehl (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)


We show that the category of algebraically cofibrant objects in a combinatorial and simplicial model category $\mathcal{A}$ has a model structure that is left-induced from that on $\mathcal{A}$. In particular, it follows that any presentable model category is Quillen equivalent (via a single Quillen equivalence) to one in which all objects are cofibrant.


model category, cofibrant object, coalgebra

2010 Mathematics Subject Classification

18C35, 55U40

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