nLab Fosco Loregian

I am an Italian postdoc.

I’m a former student of Domenico Fiorenza. I owe him my mathematical everything.

I’ve been a postdoc in all these places:

• University of Western Ontario, (CA)
• Masaryk University (CZ)
• Max Planck Institute for Mathematics (D)
• Center of Mathematics, University of Coimbra (PT)

Currently, I am in Tallinn in the compositionality group of Pawel Sobocinski.

Here’s a list of the papers I’ve written: link

This is my personal website. It’s way more up to date than this page here…

Write me an email any time!

Selected writings

On the non-concreteness of generic homotopy categories of model categories:

• Ivan di Liberti, Fosco Loregian: Homotopical algebra is not concrete, Journal of Homotopy and Related Structures 13 (2018) 673–687 [arXiv:1704.00303, doi:10.1007/s40062-018-0197-3]

On formal category theory:

• Ivan Di Liberti, Simon Henry, Mike Lieberman, Fosco Loregian, Formal category theory, course notes (2017) [pdf, pdf]

• Ivan Di Liberti, Fosco Loregian, On the unicity of formal category theories [arXiv:1901.01594]

Review of cohesion (cohesive toposes) and differential cohesion:

• Fosco Loregian, Cohesion in Rome, talk notes, Dec. 2019 (pdf, pdf)

On optics (in computer science):

• Bryce Clarke, Derek Elkins, Jeremy Gibbons, Fosco Loregian, Bartosz Milewski, Emily Pillmore, Mario Román, Profunctor optics: a categorical update, Compositionality 6 1 (2024) (arXiv:2001.07488, doi:10.32408/compositionality-6-1)

On (discrete) Grothendieck fibrations and profunctors:

• Emily Riehl and Fosco Loregian, Categorical notions of fibration, Expositiones Mathematicae 38 4 (2020) 496-514 [arXiv:1806.06129, doi:10.1016/j.exmath.2019.02.004]

On ends and coends:

• Fosco Loregian, Coend calculus, Cambridge University Press 2021 (arXiv:1501.02503, doi:10.1017/9781108778657, ISBN:9781108778657).

On t-structures and reflective factorization systems:

• Domenico Fiorenza, Fosco Loregian, $t$-Structures are normal torsion theories, Appl Categor Struct 24 (2016) 181–208 [arxiv:1408.7003, doi:10.1007/s10485-015-9393-z]

• Domenico Fiorenza, Fosco Loregian, Giovanni Marchetti, Hearts and towers in stable $\infty$-categories, J. Homotopy Relat. Struct. 14 (2019) 993–1042 [arXiv:1501.04658, doi:10.1007/s40062-019-00237-0]

• Fosco Loregian, Simone Vrili Triangulated factorization systems and t-structures, Journal of Algebra 550 (2020) 219-241 [doi:10.1016/j.jalgebra.2019.12.021]

Generalizing Lawvere theories to partial algebraic theories:

• Ivan Di Liberti, Fosco Loregian, Pawel Sobocinski, Chad Nester: Functorial semantics for partial theories [arXiv:2011.06644]

On the adjoint functor theorem in the context of lax-idempotent 2-monads:

• Nathanael Arkor, Ivan Di Liberti, Fosco Loregian, Adjoint functor theorems for lax-idempotent pseudomonads, [arXiv:2306.10389]

A formal category theoretic account of Gabriel-Ulmer dualities using KZ-doctrines:

• Ivan Di Liberti, Fosco Loregian, Accessibility and Presentability in 2-Categories, Journal of Pure and Applied Algebra 227 1 (2023) [arXiv:1804.08710, doi:10.1016/j.jpaa.2022.107155]

Related entries

• orthogonal factorization system in a derivator

• t-structure

• end

category: people