Assistant Professor

School of Mathematics and Statistics

Masaryk University

Brno 60000

Czech Republic

**bourkej@math.muni.cz**

Adjoint functor theorems for homotopically enriched categories (with Steve Lack and Lukáš Vokřínek), 2020. Preprint.

Algebraically cofibrant and fibrant objects revisited (with Simon Henry), 2020. Preprint.

Accessible aspects of 2-category theory, Journal of Pure and Applied Algebra 225(3), 2021.

Iterated algebraic injectivity and the faithfulness conjecture, Higher Structures 4(2), 2020, 183–210.

Braided skew monoidal categories (with Stephen Lack), Theory and Applications of Categories, Vol. 35, 2020, No. 2, pp 19-63.

Equipping weak equivalences with algebraic structure, Mathematische Zeitschrift, 294(3), 2020, 995-1019

Monads and theories (with Richard Garner), Advances in Mathematics 351 (2019), 1024-1071.

Free skew monoidal categories (with Stephen Lack), Journal of Pure and Applied Algebra 222 (2018), no. 10, 3255-2381.

Skew monoidal categories and skew multicategories (with Stephen Lack), Journal of Algebra 506 (2018), 237-266.

Note on the construction of globular weak omega-groupoids from types, topological spaces etc , Cahiers de topologie et geometrie differentielle categoriques Vol. LVII (2016), 281-285.

Skew structures in 2-category theory and homotopy theory , Journal of Homotopy and Related Structures 12 (2017), no. 1, 31-81.

The Gray tensor product via factorisation (with Nick Gurski), Applied Categorical Structures 25 (2017), no.4, 603–624

Algebraic weak factorisation systems II: categories of weak maps (with Richard Garner), Journal of Pure and Applied Algebra 220 (2016), no. 1, 148-174.

Algebraic weak factorisation systems I: accessible AWFS (with Richard Garner), Journal of Pure and Applied Algebra 220 (2016), no. 1, 108-147.

A cocategorical obstruction to tensor products of Gray-categories (with Nick Gurski), Theory and Applications of Categories 30 (2015), no. 11, 387-409.

Two-dimensional regularity and exactness (With Richard Garner), Journal of Pure and Applied Algebra 218 (2014), no. 7, 1346-1371.

Two-dimensional monadicity, Advances in Mathematics 252 (2014) 708-747.

A colimit decomposition for homotopy algebras in Cat, Applied Categorical Structures 22 (2014), no. 1, 13-28.

On semiflexible, flexible and pie algebras (with Richard Garner), Journal of Pure and Applied Algebra 217 (2013), no. 2, pages 293–321.

Codescent objects in 2-dimensional universal algebra , Phd Thesis, University of Sydney, 2010.

The 95th Peripatetic Seminar on Sheaves and Logic was held in Brno in April 2014. Here is the webpage and here is the conference photo.

Algebra Seminar webpage.