I am an Australian-born mathematician interested in higher categories, operads, polynomial functors and their applications. Though I am no longer in Academia, I maintain a connection with the mathematical community as the Managing Editor of the online journal Higher Structures.
Publications
- Every 2-Segal space is unitalCommunications in Contemporary Mathematics, 23(2):1-6, 2021ArXiv:1905.09580(with M. Feller, R. Garner, J. Kock and M. Proulx)
- Operadic categories and décalageAdvances in Mathematics, 377:1-23, 2021ArXiv:1812.01750(with R. Garner and J. Kock)
- Faà di Bruno for operads and internal algebrasJ. London Math. Soc. 99:919-944, 2019ArXiv:1609.03276(with J. Kock)
- Regular patterns, substitudes, Feynman categories and operadsTheory and Applications of Categories, 33:148-192, 2018ArXiv:1510.08934(with M. Batanin and J. Kock)
- Algebraic Kan extensions along morphisms of internal algebra classifiersTbilisi Mathematical Journal, 9(1):65-142, 2016ArXiv:1511.04911
- Internal algebra classifiers as codescent objects of crossed internal categoriesTheory and Applications of Categories, 30:1713-1792, 2015ArXiv:1503.07585
- Operads as polynomial 2-monadsTheory and Applications of Categories, 30:1659-1712, 2015ArXiv:1412.7599
- Polynomials in categories with pullbacksTheory and Applications of Categories, 30:533-598, 2015ArXiv:1412.7599
- Free products of higher operad algebrasTheory and Applications of Categories, 28:24-65, 2013ArXiv:0909.4722
- Multitensor lifting and strictly unital higher category theoryTheory and Applications of Categories, 28:804-856, 2013ArXiv:1209.2776(with M. Batanin and D-C. Cisinski)
- Multitensors as monads on categories of enriched graphsTheory and Applications of Categories, 28:857-932, 2013ArXiv:1106.1977
- Monads with arities and their associated theoriesJournal of Pure and Applied Algebra, 216:2029-2048, 2012ArXiv:1101.3064(with C. Berger and P-A. Melliès)
- Algebras of higher operads as enriched categoriesApplied Categorical Structures, 19(1):93-135, 2011ArXiv:0803.3594(with M. Batanin)
- Familial 2-functors and parametric right adjointsTheory and Applications of Categories, 18:665-732, 2007
- Yoneda structures from 2-toposesApplied Categorical Structures, 15:259-323, 2007
- Operads within monoidal pseudo algebrasApplied Categorical Structures, 13(5):389-420, 2005
- Generic morphisms, parametric representations and weakly cartesian monadsTheory and Applications of Categories, 13:191-234, 2004
Selected Lectures
- Operads and polynomial 2-monadsHigher Structures in Geometry and PhysicsCreswick Victoria, June 2016
- Structured colimits and polynomial functorsCT13 Macquarie University
- Weak n-categories with strict units via iterated enrichmentCanadian Math Society Summer MeetingHalifax, June 2013
- 2-bicategories of polynomialsCT11 Vancouver
- Lax monoidal categories and higher operadsCT10 Genoa
- Nerves and Lawvere theoriesPSSL 2007, Nancy
- 2-toposes and higher categoriesAustralian Math. Soc. meeting 2006, Macquarie University
- Applications of 2-categorical algebra to the theory of operadsAlpine Operad ConferenceVillars Switzerland 2006
Contact
mark dot weber dot math at gmail dot com