## John Bourke

Assistant Professor

School of Mathematics and Statistics

Masaryk University

Brno 60000

Czech Republic

**bourkej@math.muni.cz**

### Publications

Iterated algebraic injectivity and the faithfulness conjecture , 2018. Preprint.

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.

### Other things

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

### PSSL95

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.

### TEACHING

Representation Theory Notes , 2019.