Model categories

by Oleksii Nikitchenko (The Ohio State University)

Wednesday 19 Feb 2025, 17:30 → 18:30 Europe/Kiev

https://bbb.imath.kiev.ua/rooms/boh-0lk-tl9-vjx/join (ONLINE)

Model categories were introduced by Quillen to provide a natural setting for homotopy theory in different categories like topological spaces, chain complexes and simplicial sets.

In this talk, we will take a look at the definition of model category and provide 2 examples: model structure on topological spaces and chain complexes. Also, we will discuss small object argument, a powerful technique that provides factorizations of maps with useful properties in any model category.

References:

[1] W.G. Dwyer and J. Spalinski, Homotopy theories and model categories, in  Handbook of algebraic topology, 73--126, North-Holland, Amsterdam, ; MR1361887

[2] M. A. Hovey, Model categories, Mathematical Surveys and Monographs, 63, Amer. Math. Soc., Providence, RI, 1999; MR1650134

[3] P.S. Hirschhorn,  Model categories and their localizations, Mathematical Surveys and Monographs, 99, Amer. Math. Soc., Providence, RI, 2003; MR1944041