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.