Heya! I'm JS!
I am a DECRA Fellow and Lecturer (equivalent to Assistant Professor) at Macquarie University.
I previously did my DPhil/PhD at the University of Oxford, where I was at Kellogg College and a Clarendon Scholar.
Full Name: Jean-Simon Pacaud Lemay (He/Him)
From: Québec/Alberta, Canada
Email: js.lemay@mq.edu.au
Research Areas:
Pure Mathematics
Category Theory
Differential Categories
Traced Monoidal Categories
Restriction Categories
Commutative Algebra
Differential Geometry
Theoretical Computer Science
Linear Logic
Automatic Differentiaiton and Machine Learning
ORCID: https://orcid.org/0000-0003-4124-3722
I am the main moderator for the category theory mailing list (categories@mq.edu.au). To subscribe, please email me. Mailing list emails are also directly posted on the zulip forum.
Academic Career (Staff Position, Postdocs, and Education):
Academic Staff Positions
Discovery Early Career Researcher Award (DECRA) Fellow and Lecturer (equivalent to Assistant Professor) -- Macquarie University
Postdocs
Education
Doctorate in Philosophy (DPhil/PhD) in Computer Science -- University of Oxford, Kellogg College
Thesis: Revisiting Differential Categories: New Results on the Foundation of Differentiation
Supervisors: Jamie Vicary, Bob Coecke, and Luke Ong
Scholarships and Awards:
Master's of Science (M. Sc.) in Pure Mathematics -- University of Calgary
Thesis: Integral and Calculus Categories
Supervisors: Robin Cockett and Kristine Bauer
Scholarships and Awards:
Queen Elizabeth II Graduate Scholarship
Honours Bachelor of Science (B.S.) in Mathematics -- University of Ottawa
Publications:
In mathematics and theoretical computer science, authors are listed alphabetically and there is no designated lead author.
In computer science, publication in highly selective conference proceedings is regarded as more prestigious than journal publications.
For convenience, an open-source link of a pdf version is provided for each publication.
Publications (Peer-Reviewed):
JP = Journal Paper (peer-reviewed)
CP = Conference Paper published in the conference's proceedings (peer-reviewed)
[42/CP21] Reverse Faà di Bruno's Formula for Cartesian Reverse Differential Categories (PDF)
Biggin, A. & Lemay, J-S. P. (2024)
Published in the proceedings of ACT2024.
[41/CP20] An Ultrametric for Cartesian Differential Categories for Taylor Series Convergence (PDF)
Lemay, J-S. P. (2024)
Published in the proceedings of MFPS2024.
[40/CP19] Laplace Distributors and Laplace Transformations for Differential Categories (PDF)
Kerjean, M. & Lemay, J-S. P. (2024)
Published in the proceedings of FSCD2024.
[39/CP18] Combining Fixpoint and Differentiation Theory (PDF)
Galal, Z. & Lemay, J-S. P. (2024)
Published in the proceedings of LICS2024.
[38/JP21] The Rosický Tangent Categories of Algebras over an Operad (PDF)
Iknonicoff, S., Lanfranchi, M., Lemay, J-S. P. (2024)
Higher Structures
[37/CP17] Reverse Tangent Categories (PDF)
Cruttwell, G., Lemay, J-S. P. (2024)
Published in the conference proceedings of CSL2024.
[36/JP20] Classical Distributive Restriction Categories (PDF)
Cockett, R. Lemay, J-S. P. (2024)
Theory and Applications of Categories -- Special Issue dedicated to Pieter Hofstra.
Cruttwell, G., Lemay, J-S. P. (2023)
Theory and Applications of Categories
[34/JP18] Traced Monads and Hopf Monads (PDF)
Hasegawa, M., Lemay, J-S. P. (2023)
Compositionality.
[33/JP17] Hopf Monads on Biproducts (PDF)
Hasegawa, M., Lemay, J-S. P. (2023)
Theory and Applications of Categories.
[32/CP16] Cartesian Differential Kleisli Categories (PDF)
Lemay, J-S. P. (2023)
Published in the proceedings of MFPS2023.
[31/CP15] Graded Differential Categories and Graded Differential Linear Logic (PDF -- PDF with Appendix)
Lemay, J-S. P., Vienney, J.-B. (2023)
Published in the proceedings of MFPS2023.
[30/CP14] Moore-Penrose Dagger Categories (PDF)
Cockett, R., Lemay, J-S. P. (2023)
Published in the proceedings of QPL2023.
[29/CP13] Taylor Expansion as a Monad in Models of DiLL (PDF)
Kerjean, M., Lemay, J-S. P. (2023)
Published in the proceedings of LICS2023.
Ikonicoff, S. & Lemay, J-S. P. (2023).
Cahiers de topologie et géométrie différentielle catégoriques.
[27/JP15] Monoidal Reverse Differential Categories (PDF)
Cruttwell, G., Gallagher, P., Lemay, J-S. P. & Pronk, D. (2023).
Mathematical Structures in Computer Science.
[26/JP14] Linearizing Combinators. (PDF)
Cockett, R., Lemay, J-S. P. (2022).
Theory and Applications of Categories.
[25/JP13] Cartesian Difference Categories. (PDF)
Alvarez-Picallo, M. & Lemay, J-S. P. (2021).
Logical Methods in Computer Science.
[24/CP12] Coderelictions for Free Exponential Modalities. (PDF)
Lemay, J-S. P. (2021).
Published in the conference proceedings of CALCO2021.
Lemay, J-S. P. (2021).
Published in the conference proceedings of ACT2021.
[22/CP10] Cartesian Difference Categories. (PDF)
Alvarez-Picallo, M., & Lemay, J-S. P. (2021).
Published in the conference proceedings of FOSSACS2020.
[21/JP12] Tensor-Restriction Categories. (PDF)
Heunen, C., Lemay, J-S. P. (2021).
Theory and Applications of Categories.
Garner, R., Lemay, J-S. P. (2021).
Applied Categorical Structures.
Cruttwell, G., Lemay, J-S. P., Lucyshin-Wright R. (2021).
Cahiers de topologie et géométrie différentielle catégoriques.
[18/JP9] Differential Equations in a Tangent Category I: Complete vector fields, flows, and exponentials. (PDF)
Cockett, R., Cruttwell, G., Lemay, J-S. P. (2021).
Applied Categorical Structures.
Cockett, R., Lemay, J-S. P., & Lucyshyn-Wright, R. (2020).
Published in the conference proceedings of CSL2020.
[16/CP8] Reverse Derivative Categories. (PDF)
Cockett, R., Cruttwell, G., Gallagher, J., Lemay J-S. P., MacAdam B., Plotkin G., & Pronk, D. (2020).
Published in the conference proceedings of CSL2020.
Lemay, J-S. P. (2020).
Applied Categorical Structures.
Lemay, J-S. P. (2020).
Mathematical Structures in Computer Science.
[13/JP6] Differential Categories Revisited. (PDF)
Blute, R., Cockett, R., Lemay, J-S. P., & Seely R.A.G. (2019).
Applied Categorical Structures.
Lemay, J-S. P. (2019).
Published in the conference proceedings of QPL2019.
Kerjean, M., & Lemay, J-S. P. (2019).
Published in the conference proceedings of FOSSACS2019.
Lemay, J-S. P. (2019).
Logical Methods in Computer Science.
Lemay, J-S. P. (2019).
Journal of Pure and Applied Algebra.
Lemay, J-S. P. (2018).
Published in the conference proceedings of FSCD2018.
Cockett, R., & Lemay, J-S. P. (2018).
Published in the conference proceedings of MFPS2018.
Hasegawa, M. & Lemay, J-S. P. (2018).
Theory and Applications of Categories.
Lemay, J-S. P. (2018).
Theory and Applications of Categories.
[4/JP1] Integral Categories and Calculus Categories. (PDF)
Cockett, R., & Lemay, J-S. P. (2018).
Mathematical Structures in Computer Science.
[3/CP3] There is only one notion of differentiation. (PDF)
Cockett, R., & Lemay, J-S. P. (2017).
Published in the conference proceedings of FSCD2017.
Cockett, R., & Lemay, J-S. P. (2017).
Published in the conference proceedings of CSL2017.
Bagnol, M., Blute, R., Cockett, R., & Lemay, J-S. P. (2016).
Published in the conference proceedings of MFPS2016.
Preprints (Submitted to Peer-Review Journals):
[PP4] A Tangent Category Perspective on Connections in Algebraic Geometry (PDF)
Cruttwell, G., Lemay, J-S. P., & Vandenberg, E. (2024)
[PP3] Drazin Inverses in Categories (PDF)
Cockett, R., Lemay, J-S. P., & Srinivasan, P. V. (2024)
[PP2] Fundamental Theorems of Calculus and Zinbiel Algebras (PDF)
Lemay, J-S. P. (2024)
[PP1] Properties and Characterisations of Cofree Cartesian Differential Categories (PDF)
Lemay, J-S. P. (2022)
Conference & Workshop Presentations:
[T.54] Foundational Methods in Computer Science (FMCS) 2024 (Invited Plenary Talk)
Title: Drazin Inverses in Categories
Title: Free Differential Storage Modalities
Title: An Ultrametric for Cartesian Differential Categories for Taylor Series Convergence
Title: Reverse Faà di Bruno's Formula for Cartesian Reverse Differential Categories
[T.50] Differential λ-Calculus and Differential Linear Logic, 20 Years Later (Invited Plenary Talk)
Title: Differential Categories
Title: Hopf Monads on Biproducts
Title: Zinbiel Algebras and the Fundamental Theorems of Calculus
Title: Integrations in Differential Categories
Title: Moore-Penrose Dagger Categories
Title: Taylor Expansion as a Monad in Models of DiLL
[T.44] International Workshop on Quantitative Logical Methods (QUALOG) 2023 (Invited Contributed Talk)
Title: A Taylor Series Metric for Cartesian Differential Categories
Title: Cartesian Differential Kleisli Categories
[T.42] Conference on Algebra and Coalgebra in Computer Science (CALCO) 2023 -- Special Session on Category Theory in Machine Learning (Invited Plenary Talk)
Title: Differential Categories and Machine Learning
Title: Classical Distributive Restriction Categories
[T.40] Canadian Mathematical Society (CMS) Summer Meeting 2023 -- Hopf Algebra Scientific Session
Title: Lifting Trace with Hopf Algebras and Hopf Monads
Title: Classical Distributive Restriction Categories
[T.38] KTGU Mathematics Workshop for Young Researchers (Invited Plenary Talk)
Title: Tangent Categories: A Bridge between Differential Geometry and Algebraic Geometry
Title: The Fundamental Theorems of Calculus and Zinbiel Algebras
Title: Uniqueness of Differentiation in Differential Categories
Title: Copromotion and Taylor Approximation
Title: Monoidal Reverse Differential Categories
[T.33] Foundational Methods in Computer Science (FMCS) 2022 (Invited Plenary Talk)
Title: Tangent Categories and Algebraic Geometry
Title: Algebraic Geometry and Tangent Categories
[T.31] Novemberfest 2021
Title: Hopf Monads and Traced Monads
Title: Coderelictions for Free Exponential Modalities
Title: Tensor Restriction Categories.
Title: Jacobians and Gradients for Cartesian Differential Categories.
Title: Linearizing Combinators.
[T.26] Banff International Research Station (BIRS) Workshop on Tangent Categories and their Applications (Invited Plenary Talk)
Title: The World of Differential Categories: A Tutorial on Cartesian Differential Categories.
[T.25] Joint PPS - PIHOC - DIAPASoN Workshop 2021 (Invited Plenary Talk)
Title: Introduction to Reverse Derivative Categories.
Title: The Theory of Differential Categories. (4 tutorial lectures)
Title: What the heck is the reverse derivative?
[T.22] Yorkshire and Midlands Category Theory Seminar (YAMCATS) 2020 (Invited Plenary Talk)
Title: Characterizing Cofree Cartesian Differential Categories.
Title: Reverse Derivative Categories.
Title: Tangent Categories from the Coalgebras of Differential Categories.
Title: Exponential Functions for Cartesian Differential Categories.
Title: Tangent Categories from the Coalgebras of Differential Categories.
Title: Why FHilb is NOT an interesting (co)differential category.
[T.16] Canadian Mathematical Society (CMS) Summer Meeting 2019 -- Category Theory Scientific Session (Invited Contributed Talk)
Title: The Poincaré Lemma for Codifferential Categories with Antiderivatives. (Invited Talk)
[T.15] Foundational Methods in Computer Science (FMCS) 2019 (Invited Plenary Talk)
Title: Tutorials on differential categories and Cartesian differential categories.
Title: Why FHilb is NOT an interesting differential category.
Title: Lifting Coalgebra Modalities and IMELL Model Structure to Eilenberg-Moore Categories.
Title: Cartesian Integral Categories and Contextual Integral Categories.
[T.11] Canadian Mathematical Society (CMS) Summer Meeting 2018 -- Category Theory Scientific Session (Invited Contributed Talk)
Title: Differential Categories and Representable Tangent Categories.
Title: A Tangent Alternative to the Faa Di Bruno Construction.
[T.9] ChoCoLa Meeting Spring 2018 (Invited Plenary Talk)
Title: Differential Algebras in Differential Categories.
[T.8] DuskoFest Workshop 2017
Title: The Story of Differential Categories
Title: There is only one notion of differentiation.
Title: Integral Categories and Calculus Categories.
Title: Integration for Tangent Categories.
Title: There is only one notion of differentiation.
Title: Introduction to Tensor Integral Categories.
Title: Introduction to Cartesian Integral Categories.
Title: Introduction to Monoidal Integral Categories.
Seminar Talks:
Title: Tangent Categories
Title: Lifting Trace with Hopf Algebras and Hopf Monads
Title: Classical Distributive Restriction Categories
Title: Drazin Inverses in Categories
Title: A tour around the world of differential categories
Title: Tutorial on Differential Categories
Title: Free Differential Storage Modalities
Title: Drazin Inverses in Additive Categories and Fitting's Results
Title: On Leinster’s Eventual Image Duality (and the relation to Drazin inverses)
Title: Drazin Inverses in Categories
Title: The Fundamental Theorems of Calculus and Zinbiel Algebras
Title: Classical distributive restriction categories
Title: Algebras of classified restriction categories
Title: Classical distributive restriction categories
Title: Traced monads and Hopf monads
Title: Moore-Penrose Dagger Categories
Title: Moore-Penrose Dagger Categories
Title: A tour around the world of differential categories
Title: A tour around the world of differential categories
Title: A tour around the world of differential categories
Title: A tour around the world of differential categories
Title: Monoidal Closed but not Compact Closed
Title: Building Cartesian Differential Categories as Kleisli Categories
Title: The Fundamental Theorems of Calculus and Zinbiel Algebras
Title: Characterizing Cofree Cartesian Differential Categories
Title: On the coalgebras of a differential category and how to construct coderelictions from coalgebra structure
Title: Hopf Monads and Trace Monads
Title: Exponential Functions in a Cartesian Differential Category
Title: When is a Hopf Monad a Trace Monad?
Title: Hyperbolic Functions for Cartesian Differential Categories
Title: The symmetric algebra’s other universal properties
Title: Introduction to Cartesian Differential Categories
Title: Exponential Functions for Cartesian Differential Categories
Title: The Missing Link Between Hopf Monads and Star‑Autonomous Monads
Title: Introduction to Cartesian Differential Categories
Title: Differential Algebras in Codifferential Categories
Title: Introduction to Differential Categories
Title: What is Category Theory?
Title: Differential Categories Revisited
Title: Lifting Coalgebra Modalities
Title: Integral Category Structure of Smooth Functions
Supervision:
Undergraduate Students:
Aaron Biggin, Summer Vacation Research Project (Jan-Feb 2024)
Conference Organizations and Commitees:
Local Organizer:
Workshop on Categorical Structures in Computer Science -- Local Organizer (Workshop at RIMS)
Third Symposium on Compositional Structures (SYCO3) -- Local Chair
Kellogg College Student Colloquium 2018/2019 (Weekly Graduate Student Seminar)
University of Calgary Mathematics Graduate Colloquium 2017/2018 (Weekly Graduate Student Seminar)
Program Committee:
Award Committee:
Editorial Responsibilities:
Editor:
Special issue of Mathematical Structures in Computer Science on "Differential Structures in Computer Science and Mathematics"
Teaching:
Macquarie University
Semester 1 2024: Lecturer for Algebra IIIA
University of Oxford, New College
A college tutor is equivalent to a teaching assistant at other universities.
Hilary 2021: New College Tutor for "Categorical Quantum Mechanics"
Michaelmas 2020: New College Tutor for "Homological Algebra"
University of Oxford, Computer Science Department
A tutor is equivalent to a teaching assistant at other universities, while a teaching assistant is equivalent to a marker at other universities.
Hilary 2020: Lecturer for "Categorical Quantum Mechanics"
Michaelmas 2020: Tutor for "Categories, Proofs and Processes" and "Quantum Processes and Computation"
University of Oxford, Mathematics Institute
A tutor is equivalent to a teaching assistant at other universities, while a teaching assistant is equivalent to a marker at other universities.
Michaelmas 2020: Tutor for "Category Theory"
Hilary 2019: Tutor for "Set Theory" (x2)
Hilary 2018: Teaching Assistant for "Introduction to Quantum Information"
Michaelmas 2018: Teaching Assistant for "Logic"
University of Calgary, Mathematics Department
Winter 2017: Teaching Assistant for "Vector Calculus for Eng. & Sci" (x2) and "Calculus III", and Marker for "Analysis"
Winter 2016: Teaching Assistant for "Linear Methods I" (x2), and Drop-in Sessions for "Discrete Math" and "Linear Algebra I"
Spring 2016: Teaching Assistant for "Linear Methods I" (x2) and "Linear Methods II"
Fall 2016: Teaching Assistant for "Linear Methods I" (x2) and "Linear Methods II" (x2), and Drop-in Sessions for "Linear Methods I"
Fall 2015: Teaching Assistant for "Calculus I" (x2) and "Linear Methods I" (x2), and Drop-in Sessions for "Calculus"
University of Ottawa, Mathematics Department
Winter 2015: Teaching Assistant for "Calculus II"
I'm also a big fan of these sports teams!
Montreal Canadiens
Calgary Flames
