Contact me mszyld@dal.ca, Research Interests Category theory and its applications. In particular the extension to higher category theory of basic categorical concepts and results. 2-dimensional category theory, in particular bicategories and double categories. Representation theory. In particular Galois and Tannaka theories, especially for topos. Events 2021, Categories and Topology, Special session at Mathematical Congress of the Americas, Schedule and abstracts, videos of the talks. Co-organized with Eduardo Dubuc and Dorette Pronk. Publications 2022, Model bicategories and their homotopy bicategories (joint with Descotte M.E. and Dubuc E. J.), Advances In Mathematics 404. arXiv:1805.07749. 2020, A localization of bicategories via homotopies (joint with Descotte M.E. and Dubuc E. J.), Theory and Applications of Categories 35, 23, p.845-874. arXiv: 1805.05248. 2019, Lifting PIE limits with strict projections, Theory and Applications of Categories 34, 1, p.1-12. arXiv: 1809.04712.

• 2018, A general limit lifting theorem for 2-dimensional monad theory, Journal of Pure and Applied Algebra 222, 8, p.2359-2373. arXiv version:1702.03303.
• 2018, Sigma limits in 2-categories and flat pseudofunctors (joint with Descotte M.E. and Dubuc E. J.), Advances in Mathematics 333, p. 266-313. arXiv: 1610.09429.
• 2018, A construction of certain weak colimits and an exactness property of the 2-category of categories (joint with Descotte M.E. and Dubuc E. J.), Theory and Applications of Categories 33, 8, p.192-215. arXiv version:1610.02453.
• 2016, Tannaka theory over sup-lattices and descent for topoi (joint with Dubuc E. J.), Theory and Applications of Categories 31, p.852-906.
• 2013, A Tannakian Context For Galois Theory (joint with Dubuc E. J.), Advances In Mathematics 234, p. 528-549. arXiv:1110.6411.

Preprints

Talks

• (June 4) "On Tannaka Recognition and Descent for Topoi" (joint work with Eduardo Dubuc) at the Descent Methods in Algebra, Geometry, and Topology session, in the 2022 CMS Summer Meeting, abstract.
• (May 24) Seminar talk "An invitation to double categories and double fibrations" (joint work with Geoff Cruttwell, Michael Lambert, and Dorette Pronk) at the Algebra, Logic and Topology Seminar (CENTRE FOR MATHEMATICS, UNIVERSITY OF COIMBRA)
• (March 1st) Seminar talk "Double Fibrations (or functors are categories)" (joint work with Geoff Cruttwell, Michael Lambert, and Dorette Pronk) at the ATCAT Seminar (abstract).

• (October 20) Seminar talk "Categories for the Learning Mathematician" at the Dalhousie Honours Seminar (abstract).
• (October 12) Seminar talk "Minimal Bicategories of Fractions and Colimits of Bicategories" (joint work with P. Bustillo and D. Pronk) at the ATCAT Seminar (abstract).
• (August 30, Hybrid) Online talk "Lifting PIE limits with strict projections" at CT 20->21 - International Category Theory Meeting Genoa (Italy), video, abstract.
• (April 7, Zoom) Seminar talk "The three F's in bicategory theory" (joint work with P. Bustillo and D. Pronk) at the UNAM Seminar (abstract).
• (March 23, Zoom) Seminar talk "The three F's in bicategory theory" (joint work with P. Bustillo and D. Pronk) at the ATCAT Seminar (abstract).

• (October 27th, Zoom) Seminar talk "Model bicategories and their homotopy bicategories" (joint work with Descotte M.E. and Dubuc E. J.) at the ATCAT Seminar (abstract and slides).
• (October 22nd, Zoom) Seminar talk "The Grothendieck Construction for Double Categories" (joint work with M. Bayeh and D. Pronk) at the uOttawa logic seminar (abstract, slides).
• (March 3rd) Seminar talk "Sigma limits in 2-categories and applications" (partially joint work with Descotte M.E. and Dubuc E. J.) at the ATCAT Seminar at Dalhousie University. (abstract, slides, note it may take a while to load the slides).

• Sigma limits and applications at CT OctoberFest 2018 , CUNY in New York, USA (abstract, slides).
• Homotopy for weak equivalences at CT2018 - International Category Theory Meeting, at UAc in Ponta Delgada, Portugal (abstract, slides).
• Seminar talk at the Categories superieures, polygraphes et homotopie seminar at Paris Diderot, France (abstract).
• Seminar talk at the Homotopie en Geometrie Algebrique seminar at the Institut de Mathematiques de Toulouse, France (abstract).

• At CT2017 - International Category Theory Meeting, at UBC in Vancouver, Canada (abstract, slides).
• limit lifting at XXVI ERAG at ICAS in Buenos Aires, Argentina (spanish abstract, spanish slides).
• At the 5th Workshop on Categorical Methods in Non-Abelian Algebra, UCL in Louvain-la-Neuve, Belgium (abstract, slides).
• At the Categories superieures, polygraphes et homotopie seminar at Paris Diderot, France (abstract).

• 2016: At OU Algebra and Representation Theory Seminar, in Oklahoma, USA, "On flat functors" (abstract).
• 2016: At UCO Math club in Oklahoma, USA, "The universal properties that lie behind the objects" (abstract).
• 2014: A short course on "Classifying Topoi and Galois Theory" (spanish abstract) and a conference "Relations in a topos: a new example of a Tannakian category" (spanish abstract) at UNEMAT 2014 in Bogota, Colombia.
• 2012: Tannakian techniques in topos representation theory at IV Latin American Meeting at UNC in Cordoba, Argentina (abstract)
• 2011: A Tannakian context for Galois at XXI Encuentro Rioplatense de Algebra y Geometria at CMAT in Montevideo, Uruguay, (slides)
• 2010: A Tannakian approach to Grothendieck Galois theory at elENA V and at the annual UMA reunion (slides) in Argentina.