nLab John Bourke

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• MathematicsGenealogy page

Selected writings

• cf.: list of arXiv preprints

On codescent objects in 2-dimensional universal algebra:

• John Bourke: Codescent objects in 2-dimensional universal algebra, PhD thesis, Sydney (2010) [pdf, pdf]

On 2-category theoretic notions of exact categories:

• John Bourke, Richard Garner: Two-dimensional regularity and exactness, Journal of Pure and Applied Algebra, 218 7 (2014) 1346–1371 [doi:10.1016/j.jpaa.2013.11.021, arXiv:1304.5275]

On skew-monoidal categories:

• John Bourke, Stephen Lack, Skew monoidal categories and skew multicategories, Journal of Algebra 506 (2018), 237-266. [arXiv:1708.06088, doi:10.1016/j.jalgebra.2018.02.039]

Examples of skew-closed monoidal structures on model categories which become monoidal on the homotopy category:

• John Bourke, Skew structures in 2-category theory and homotopy theory, J. Homotopy Relat. Struct. 12 1 (2017) 31-81 [arXiv:1510.01467, doi:10.1007/s40062-015-0121-z]

Skew monoidal closed structures on the category of Gray categories:

• John Bourke, Gabriele Lobbia, A skew approach to enrichment for Gray-categories, Advances in Mathematics 434 (2023) [arXiv:2212.12358, doi.org/10.1016/j.aim.2023.109327]

On algebraic weak factorization systems:

• John Bourke, An orthogonal approach to algebraic weak factorisation systems, Journal of Pure and Applied Algebra 227 6 (2023) 107294 [arxiv:2204.09584, doi:10.1016/j.jpaa.2022.107294]

Skew monoidal closed structures on the category of Gray categories are considered in:

• John Bourke, Gabriele Lobbia, A skew approach to enrichment for Gray-categories, (2022). [arXiv:2212.12358]

category: people