I am an Australian-born mathematician working on higher categories, operads, polynomial functors and their applications. Until recently (the end of January 2018) I was visiting the Faculty of Mathematics and Physics of Charles University in Prague, supported by the Eduard Čech Institute. I am also the Managing Editor of the new online journal Higher Structures.

E-mail mark dot weber dot math at gmail dot com

Publications

• Generic morphisms, parametric representations and weakly cartesian monads. Theory and Applications of Categories, 13:191-234, 2004.

• Operads within monoidal pseudo algebras. Applied Categorical Structures, 13(5):389-420, 2005.

• Yoneda structures from 2-toposes. Applied Categorical Structures, 15:259-323, 2007.

• Familial 2-functors and parametric right adjoints. Theory and Applications of Categories, 18:665-732, 2007.

• (with M. Batanin), Algebras of higher operads as enriched categories. Applied Categorical Structures, 19(1):93-135, 2011.

• (with C. Berger and P-A. Melliès), Monads with arities and their associated theories. Journal of Pure and Applied Algebra, 216:2029-2048, 2012.

• Multitensors as monads on categories of enriched graphs. Theory and Applications of Categories, 28:857-932, 2013.

• (with M. Batanin and D-C. Cisinski), Multitensor lifting and strictly unital higher category theory. Theory and Applications of Categories, 28:804-856, 2013.

• Free products of higher operad algebras. Theory and Applications of Categories, 28:24-65, 2013.

• Polynomials in categories with pullbacks. Theory and Applications of Categories, 30:533-598, 2015.

• Operads as polynomial 2-monads. Theory and Applications of Categories, 30:1659-1712, 2015.

• Internal algebra classifiers as codescent objects of crossed internal categories. Theory and Applications of Categories, 30:1713-1792, 2015.

• Algebraic Kan extensions along morphisms of internal algebra classifiers, Tbilisi Mathematical Journal, 9(1):65-142, 2016.

• (with M. Batanin and J. Kock), Regular patterns, substitudes, Feynman categories and operads, Theory and Applications of Categories, 33:148-192, 2018.

Preprints

• (with J. Kock), Faà di Bruno for operads and internal algebras, arXiv:1609.03276, 25 pages, 2016.

• (with R. Garner and J. Kock), Operadic categories and décalage, arXiv:1812.01750, 20 pages, 2018.

Talks

• Applications of 2-categorical algebra to the theory of operads, Notes for a talk at the Alpine Operad Conference, Villars Switzerland, 2006.

• 2-toposes and higher categories, talk slides, Australian Math. Soc. meeting 2006, Macquarie University.

• Nerves and Lawvere theories, talk slides, PSSL meeting 2007, Nancy.

• Lax monoidal categories and higher operads, talk slides, CT10, Genoa.

• 2-bicategories of polynomials, talk slides, CT11, Vancouver.

• Weak n-categories with strict units via iterated enrichment, talk slides, Canadian Math Society summer meeting, Halifax, June 2013.

• Structured colimits and polynomial functors, talk slides, CT13, Sydney.

• Operads and polynomial 2-monads, talk slides, Higher Structures in Geometry and Physics, Creswick Victoria, June 2016.