Department of Philosophy
Carnegie Mellon University
Pittsburgh, PA  15213

Office: Baker Hall 148

email :

Category theory course 80-413/713

Pittsburgh's HoTT seminar

Gathered thoughts

A view to mathematics


Things about me

I'm a french researcher in mathematics currrently working in Steve Awodey's group in CMU.

I'm a geometer with various interests:

  • ∞-category theory, the set theory of XIX century;
  • algebraic geometry, the study of spaces by means of algebras of functions;
  • ∞-topos theory, the algebraic geometry of functions with values in infinity-groupoids;
  • categorical Logic and its relationships to topology and geometry;
  • symplectic geometry and its use in the mathematization of physics;
  • philosophical reflection on mathematics, mainly in connection with Kant philosophy.



Things with theorems

- A paper about the small object argument for unique factorization systems with applications to left-exact localizations of topoi (2020, joint work with C. Leena Subramaniam).

- An application of the previous paper to Goodwillie theory (2017, joint work with G. Biedermann, E. Finster and A. Joyal).

- A paper on the Blakers-Massey theorem (2017, joint work with G. Biedermann, E. Finster and A. Joyal)

- A paper on the cofree coalgebra over a cooperad (2014)

- My book with André Joyal on Sweedler theory of (co)algebras and the bar-cobar constructions (2013)

- More on arXiv



Things with ideas

- Slides of a lecture on enveloping infinity-topoi (MURI meeting, March 2020)

- Slides of my lectures HoTT 2019 -- Summer School (Lecture I) (August 2019)

- Slides of my HoTTEST seminar Univalence & Descent (May 2019)

- Slides of a talk on What is a space? (April 2019, 6th workshop on formal topology)

- Table of contents of a book I'm editing with Gabriel Catren on New Spaces in Mathematics and Physics -- Formal and Conceptual Reflections (to be edited this year by Cambridge University Press)

Two chapters for the book:
- Introduction to the geometric aspects of topos theory: Topo-logie (2019, written with André Joyal)
- An introduction to Derived Geometry: The geometry of ambiguity (2016)

- Slides about the sequel of my joint work with Georg Biederman, Eric Finster and André Joyal on left exact localizations of topos and Goodwillie calculus (2018, talk at YaMCATS & PSSL 103)

- Slides from three lectures on topoi in Nice (2018, in french)

- The slides from a talk about Why higher categories are useful (2017, in french)

- More slides of our work with André Joyal on bar-cobar constructions

- Slides of André Joyal's talk at the AMS meeting (2012 Boston) on our work on bar-cobar constructions

- A note about why deformations are cohomological (2010)

- Introductory notes to derived categories (2010, in french)



Things to watch

- Video from my talk at the Oktoberfest, in Baltimore Small object argument for unique factorization systems (2019)

- Video from my talk at HoTTEST seminar on Univalence & Descent (2019)

- Video from a talk in IHES about Toposes as commutative rings (2015)

- Video from a conference in IHP about Derived geometry (2015)

- Video from a workshop in Paris 7 about the evolution of homological algebra beyond the vision of Grothendieck (2015, in french)

- Video from a workshop in Paris 7 about Ambiguity in Mathematics (2014)



Things for fun

- Slides from a popularization talk about Cross-multiplication (2017, in french)



Things for philosophers

- Slide of a talk at the seminar Semiomath explaining how homotopy theory is a substitute for set theory: The homotopy quotient (2018)

- Slide of a talk at the seminar (Id)entification::(Id)entité about the mathematics of identification (2016, in french)


all pictures are copyrighted