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Some Constructions of Algebraic Model Categories

Bainbridge, Gabriel
http://orcid.org/0000-0002-3386-5815
http://rave.ohiolink.edu/etdc/view?acc_num=osu1620719585729611

Abstract Details

2021, Doctor of Philosophy, Ohio State University, Mathematics.
We show that for a large class of algebraic model categories, the compact algebraic model categories, the projective model structure on the functor category of any diagram exists and is an algebraic model category. For a large class of these compact algebraic model categories, the projective algebraic model structures themselves will be compact. This generalizes a result for cofibrantly generated algebraic model categories. To prove our result, we fix an issue with and generalize Garner's construction of free algebraic weak factorization systems and more fully develop the theory of algebraic model categories. We then present an easy proof that the h-model structure on k-spaces is a compact algebraic model structure. This gives a method for computing homotopy colimits of any shape of diagram in the h-model structure. We also define quasiaccessible categories, which both generalize locally presentable categories and include the categories of topological spaces and k-spaces. We define quasiaccessible model structures on quasiaccessible categories, prove they have associated algebraic model structures, and show how the Bousfield-Friedlander theorem can be applied to produce a Bousfield localization of a quasiaccessible category that is itself an algebraic model category. We then prove that the h-model structure on topological spaces is a quasiaccessible model structure. We conclude with a characterization of certain accessible model categories inspired by Smith's theorem for combinatorial model categories. The results of this thesis provide general methods for dealing with large classes of noncofibrantly generated model structures on reasonably well-behaved categories.
Sanjeevi Krishnan, Dr (Advisor)
John Harper, Dr (Committee Member)
Crichton Ogle, Dr (Committee Member)
240 p.
Mathematics
free monads; free monoids; algebraic weak factorization systems; algebraic model categories; cofibrant generation; small object argument; projective model structure; lifting model structures; accessible categories

Recommended Citations

Citations

  • Bainbridge, G. (2021). Some Constructions of Algebraic Model Categories [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1620719585729611

    APA Style (7th edition)

  • Bainbridge, Gabriel. Some Constructions of Algebraic Model Categories. 2021. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1620719585729611.

    MLA Style (8th edition)

  • Bainbridge, Gabriel. "Some Constructions of Algebraic Model Categories." Doctoral dissertation, Ohio State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1620719585729611

    Chicago Manual of Style (17th edition)

osu1620719585729611
142
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This open access ETD is published by The Ohio State University and OhioLINK.