Rory B. B. Lucyshyn-Wright

Associate Professor
Department of Mathematics and Computer Science
Brandon University
Brandon, Manitoba, Canada

Assistant Professor (term), Mount Allison University (2017-2018)
AARMS Postdoctoral Fellow, Mount Allison University (2015-2017)
NSERC Postdoctoral Fellow, University of Cambridge (2014-2015), University of Ottawa (2013-2014)

Publications and preprints

• V-graded categories and V-W-bigraded categories: Functor categories and bifunctors over non-symmetric bases. Preprint (2025). arXiv:2502.18557
• Enriched structure–semantics adjunctions and monad–theory equivalences for subcategories of arities (with J. Parker). Theory and Applications of Categories 41 (2024), 1873-1918. arXiv:2305.07076
• Diagrammatic presentations of enriched monads and varieties for a subcategory of arities (with J. Parker). Applied Categorical Structures 31 (2023). arXiv:2207.05184
• Centralizer clones relative to a strong limit cardinal (with D. McLaren). Preprint (2022). arXiv:2209.14425
• Presentations and algebraic colimits of enriched monads for a subcategory of arities (with J. Parker). Theory and Applications of Categories 38 (2022), 1434-1484. arXiv:2201.03466
• Bifold algebras and commutants for enriched algebraic theories. Applied Categorical Structures 30 (2022), 1077-1121. arXiv:2108.03537
• Locally bounded enriched categories (with J. Parker). Theory and Applications of Categories 38 (2022), 684-736. arXiv:2110.07072
• Integral and differential structure on the free C^∞-ring modality (with G. S. H. Cruttwell and J.-S. P. Lemay). Cahiers de Topologie et Géométrie Différentielle Catégoriques LXII (2021), 116-176. arXiv:1902.04555
• Tangent categories from the coalgebras of differential categories (with J. R. B. Cockett and J.-S. P. Lemay). Proceedings of CSL 2020, in: Leibniz International Proceedings in Informatics 152 (2020), 17:1-17:17. arXiv:1910.05617
• Affine geometric spaces in tangent categories (with R. F. Blute and G. S. H. Cruttwell). Theory and Applications of Categories 34 (2019), 405-437. arXiv:1807.09554
• A simplicial foundation for differential and sector forms in tangent categories (with G. S. H. Cruttwell). Journal of Homotopy and Related Structures 13 (2018), 867-925. arXiv:1606.09080
• Commutants for enriched algebraic theories and monads. Applied Categorical Structures 26 (2018), 559-596. arXiv:1604.08569
• Convex spaces, affine spaces, and commutants for algebraic theories. Applied Categorical Structures 26 (2018), 369-400. arXiv:1603.03351
• On the geometric notion of connection and its expression in tangent categories. Theory and Applications of Categories 33 (2018), 832-866. arXiv:1705.10857
• Functional distribution monads in functional-analytic contexts. Advances in Mathematics 322 (2017), 806-860. arXiv:1701.08152
• Enriched algebraic theories and monads for a system of arities. Theory and Applications of Categories 31 (2016), 101-137. arXiv:1511.02920
• Relative symmetric monoidal closed categories I: Autoenrichment and change of base. Theory and Applications of Categories 31 (2016), 138-174. arXiv:1507.02220
• Derivations in codifferential categories (with R. Blute and K. O'Neill). Cahiers de Topologie et Géométrie Différentielle Catégoriques LVII (2016), 243-280. arXiv:1505.00220
• Completion, closure, and density relative to a monad, with examples in functional analysis and sheaf theory. Theory and Applications of Categories 29 (2014), 896-928. arXiv:1406.2361
• Enriched factorization systems. Theory and Applications of Categories 29 (2014), 475-495. arXiv:1401.0315
• A general Fubini theorem for the Riesz paradigm. Preprint. arXiv:1210.4542
• Algebraic theory of vector-valued integration. Advances in Mathematics 230 (2012), 552-576. arXiv:1108.2913
• Totally distributive toposes. Journal of Pure and Applied Algebra 216 (2012), 2425-2431. arXiv:1108.4032
• Domains occur among spaces as strict algebras among lax. Mathematical Structures in Computer Science 21 (2011), 647-670.
• Kleisli Monoids (with D. Hofmann, R. Lowen, G.J. Seal). In: D. Hofmann, G.J. Seal, W. Tholen (Eds.), Monoidal Topology, Cambridge University Press, 2014.

PhD thesis

• Riesz-Schwartz extensive quantities and vector-valued integration in closed categories
  
  • Defended June 18, 2013, York University, Canada.
  • Supervisor: Walter Tholen, External examiner: F. William Lawvere.

Teaching

Brandon University

• Measure and Integration, Winter 2024
• Modern Algebra II, Winter 2024
• Modern Algebra I, Fall 2023
• Introduction to Set Theory and Logic, Fall 2023
• Measure and Integration, Winter 2023
• Modern Algebra II, Winter 2023
• Modern Algebra I, Fall 2022
• Introduction to Set Theory and Logic, Fall 2022
• Measure and Integration, Winter 2022
• Modern Algebra, 2021-2022
• Introduction to Set Theory and Logic, Fall 2021
• Measure and Integration, Winter 2021
• Modern Algebra, 2020-2021
• Advanced Topics in Mathematics - Category Theory and General Algebra, 2020-2021
• Introduction to Set Theory and Logic, Fall 2020
• Measure and Integration, Winter 2020
• Modern Algebra, 2019-2020
• Introduction to Set Theory and Logic, Fall 2019
• Calculus IV, Winter 2019
• Modern Algebra, 2018-2019
• Introduction to Set Theory and Logic, Fall 2018

• Complex Variables, Winter 2018
• Numerical Analysis, Winter 2018
• Calculus I, Sections A and B, Fall 2017
• Real Analysis I, Fall 2016
• Calculus I, Fall 2015

• Category Theory, Master's (Part III) course, Fall 2014

• Introduction to Mathematical Logic, Winter 2014

• Integral Calculus with Applications, Fall 2012