Axel Osmond

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)

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

Work in progress

• Appendice to Factorizing systems and Kan extensions  (with Olivia Caramello)

• Point-free sheaf representation and Gelfand rings  (with Bernhard Banaschewski, Mai Gehrke & Sam van Gool)

• 2-dimensional topos theory

• 2-dimensional spectral construction: a geometry of semantics

PhD thesis

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

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)

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)