Axel Osmond

Publications and preprints

• On Diers theory of Spectrum I : Stable functors and right multi-adjoints 

• On Diers theory of Spectrum II :  Geometries and dualities 

• The spectral site, revisited 

• On coslices and commas of locally finitely presentable categories

• Local right biadjoints, bistable pseudofunctors and bifactorization 2-geometries for Grothendieck topoi

• The over-topos at a model (with Olivia Caramello), published in TAC, volume 39, 447-492 (2023)

• Bi-accessible and bipresentable 2-categories (with Ivan di Liberti), published in Applied Categorical Structures, Volume 33, article number 3 (2025)

• Codescent and bicolimits of pseudo-algebras, published in Applied Categorical Structures, Volume 32, article number 11 (2024)

• On a (terminally connected, pro-etale) factorization for geometric morphisms (with Olivia Caramello)

• Morphisms and comorphisms of sites I - Double category of sites (with Olivia Caramello), published in Applied Categorical Structures, Volume 34, article number 24, (2026)

• Morphisms and comorphisms of sites II - Distributors of sites (with Olivia Caramello)

PhD thesis

• A categorical study of spectral dualities, (Une étude catégorique des dualités spectrales), PhD thesis, December 2021

Programmation

• hypypyp, a python library to work in the category of hypergraphs.

Talks

• General construction of spectra : Overview and perspectives, contributed talk at TACL 2019 

• Towards a 2-dimensional spectral construction, Masaryk University Algebra Seminar,  mai 2020

• The over-topos at a model (joint work with Olivia Caramello), contributed talk at Topos Online, June 2021

• Stable pseudofunctors, local right bi-adjoints and 2-geometries for topoi, onsite contributed talk at CT20->21, September 2021

• Bistable pseudofunctors and bifactorization 2-geometries for Grothendieck topoi,  CaTCAT 2021, Mexico, November 2021

• Bi-accessible and bipresentable 2-categories, Australian Category Seminar, April 2022

• First order doctrines as finitely bipresentable 2-categories, contributed talk at TACL, 2022

• Spectres et géométries, présentation au Groupe de travail Catégories, LIPN, Université Paris XIII, Octobre 2022

• Théorie catégorique des constructions spectrales, Groupe de travail Lectures topossiques, Centre Lagrange, 2023 (Slides 1ère séance; slides 2nde séance; slides 3ème séance)

• MV-algebras and their geometry, Groupe de travail Lectures topossiques, Centre Lagrange,  5 avril 2024 (slides)

• On a (terminally connected, pro-etale) factorization for geometric morphisms, Groupe de travail Lectures topossiques, Centre Lagrange,  26 mai 2024

• On a (terminally connected, pro-etale) factorization for geometric morphisms, contributed talk at CT2024, Santiago de Compostela

• Morphisms and comorphisms of sites: double-categorical and profunctorial aspects, invited talk at Topos in Mondovi, September 2024

• Morphisms and comorphisms of sites: a double-categorical approach, contributed talk at CT2025, Brno

Music theory

• Undecimarvelous (11-limit just-intonation temperament related to the 7-limit Marvelous temperament)

• Undecimus (10 steps 11-limit JI temperament)

• Undecimus' (another 10 steps 11-limit JI temperament)