Clark Barwick (changes) in nLab

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• website

Selected writings

On (∞,n)-categories:

• Clark Barwick, (∞,n)(\infty,n)-CatCat as a closed model category PhD (2005)

On Bousfield localization of combinatorial model categories:

• Clark Barwick, On left and right model categories and left and right Bousfield localizations, Homology, Homotopy and Applications 12 2 (2010) 245–320 [[doi:10.4310/hha.2010.v12.n2.a9](https://doi.org/10.4310/hha.2010.v12.n2.a9), subsuming:euclid:1296223884, subsuming: arXiv:0708.2067, arXiv:0708.2832, arXiv:0708.3435]

On relative categories:

• Clark Barwick, Daniel Kan, Relative categories: Another model for the homotopy theory of homotopy theories. Indagationes Mathematicae 23 (2012) 42-68 [[arXiv:1011.1691](https://arxiv.org/abs/1011.1691), doi:10.1016/j.indag.2011.10.002]

On models for (∞,n)-categories:

• Clark Barwick, Chris Schommer-Pries, On the Unicity of the Homotopy Theory of Higher Categories (arXiv:1112.0040, slides)

On simplicial localization as a functor on the category of relative categories:

• Clark Barwick, Daniel Kan, A characterization of simplicial localization functors and a discussion of DK equivalences, Indagationes Mathematicae Volume 23, Issues 1–2, March 2012, Pages 69-79 (doi:10.1016/j.indag.2011.10.001)

On exact (∞,1)-categories:

• Clark Barwick, On the Q construction for exact quasicategories (arXiv:1301.4725)

and the theorem of the heart:

• Clark Barwick, On exact infinity-categories and the Theorem of the Heart, Compositio Mathematica 151 (2015) 2160-2186 [[arXiv:1212.5232](https://arxiv.org/abs/1212.5232), doi:10.1112/S0010437X15007447]

On spectral Mackey functors and equivariant algebraic K-theory:

• Clark Barwick, Spectral Mackey functors and equivariant algebraic K-theory (I), Adv. Math., 304:646–727, 2017 (doi:10.1016/j.aim.2016.08.043, arXiv:1404.0108)

• Clark Barwick, Saul Glasman, Jay Shah, Spectral Mackey functors and equivariant algebraic K-theory (II) (arXiv:1505.03098)

On cyclotomic spectra:

• Clark Barwick, Saul Glasman, Cyclonic spectra, cyclotomic spectra, and a conjecture of Kaledin (arXiv:1602.02163)

• Clark Barwick, Saul Glasman, Noncommutative syntomic realization (pdf)

See also:

• SHIFTED: Stratified Homotopy Invariants, Field Theories, Exodromy, and Duality (github)

• Bousfield localization

• n-category

• algebraic K-theory

• cyclotomic spectrum

• Parametrized Higher Category Theory and Higher Algebra