Workshop on
Doctrines & Fibrations

Dedicated to F. William Lawvere
(February 9, 1937 – January 23, 2023)

Tutorial Speakers

• Giuseppe Rosolini (Università di Genova, Italy)
  Hyperdoctrines and logic
• Thomas Streicher (Technische Universität Darmstadt, Germany)
  Precohesive Toposes over arbitrary Base Toposes

Invited Speakers

• Steve Awodey (Carnegie Mellon University, USA)
  First steps in algebraic type theory
• Benno van den Berg (Universiteit van Amsterdam, Netherlands)
  Algebraic structures for modified realizability
• Jacopo Emmenegger (Università di Genova, Italy)
  Elementary fibrations and quotients of groupoids
• Jonas Frey (Carnegie Mellon University, USA)
  Partial equivalence relations, localizations, and equipments
• Matías Menni (Conicet and Universidad Nacional de La Plata, Argentina)
  Bi-directional models of “Radically Synthetic” Differential Geometry
• Alexandre Miquel (Universidad de la República, Uruguay)
  First-order completeness of implicative models
• Jaap van Oosten (Universiteit Utrecht, Netherlands)
  Lawvere-Tierney topologies and games
• Valeria de Paiva (Topos Institute, Berkeley, USA)
  Dialectica categories and doctrines
• Fabio Pasquali (Università di Genova, Italy)
  Relational doctrines and quotient completions
• Davide Trotta (Università di Pisa, Italy)
  Abstracting sheafification-like adjunctions via tripos-to-topos

Programme

► Playlist of video recordings of some of the talks
► Slides of some of the talks

Monday 29th

• 9:55
  Opening
• 10:00-11:00
  Rosolini (tutorial), Hyperdoctrines and logic
  chair: Streicher
• 11:00-11:30
  Break
• 11:30-12:15
  van Oosten, Lawvere-Tierney topologies and games
  chair: Maietti
• 12:15-14:45
  Lunch Break
• 14:45-15:30
  Frey, Partial equivalence relations, localizations, and equipments
  chair: Maschio
• 15:30-15:55
  Ülo Reimaa, The fibration of algebras
  chair: Maschio

Tuesday 30th

• 10:00-11:00
  Streicher (tutorial), Precohesive Toposes over arbitrary Base Toposes
  chair: Rosolini
• 11:00-11:30
  Break
• 11:30-12:15
  Benno van den Berg, Algebraic structures for modified realizability
  chair: Miquel
• 12:15-14:45
  Lunch Break
• 14:45-15:30
  Trotta, Abstracting sheafification-like adjunctions via tripos-to-topos
  chair: Frey
• 15:30-15:55
  Wrigley, Eliminating imaginaries and adding structure: how does the geometric completion fit in?
  chair: Frey

Wednesday 31st

• 10:00-10:45
  Awodey, First steps in algebraic type theory
  chair: van den Berg
• 10:45-11:15
  Break
• 11:15-12:00
  Emmenegger, Elementary fibrations and quotients of groupoids
  chair: Metere
• 12:00-14:45
  Lunch Break
• 14:45-15:30
  Pasquali, Relational doctrines and quotient completions
  chair: de Paiva
• 15:30-15:55
  Stenzel, The (∞, 2)-categorical externalization functor
  chair: de Paiva


• 20:15
  Social dinner at Ristorante Lo Zairo

Thursday 1st

• 10:00-10:45
  de Paiva, Dialectica categories and doctrines
  chair: van Oosten
• 10:45-11:15
  Break
• 11:15-11:40
  Basold, Enriched Coalgebras and Coinductive Predicates
  chair: Salibra
• 11:40-12:05
  Spadetto, Strictifying Path Categories
  chair: Salibra
• 12:05-14:45
  Lunch Break
• 14:45-15:30
  Miquel, First-order completeness of implicative models
  chair: Awodey
• 15:30-16:15
  Menni, Bi-directional models of “Radically Synthetic” Differential Geometry
  chair: Streicher
• 16:15
  Closing

Contributed Talks

• Henning Basold, Enriched Coalgebras and Coinductive Predicates
• Ülo Reimaa, The fibration of algebras
• Matteo Spadetto, Strictifying Path Categories
• Raffael Stenzel, The (∞, 2)-categorical externalization functor
• Joshua Liam Wrigley, Eliminating imaginaries and adding structure:
  how does the geometric completion fit in?

Deadline for contributions: 6th May
Acceptance: 12th May

Registration

To register, please send an email to orgwdf@math.unipd.it specifying your name and affiliation.

Deadline for registration: 26th May

Venue

• Torre Archimede, Department of Mathematics (Google Maps)
• Address: Via Trieste, 63 - 35121 Padova (Italy)
• Tel: +39 049 827 1200
• Fax: +39 049 827 1499
• E-mail: dipmath@math.unipd.it

Workshop location

The Workshop will be held in Room 2BC60 of the Department of Mathematics. To reach the room, it is most convenient to enter the building from tower B or tower C and go up to the second floor; you will find room 2BC60 in the middle of the corridor side BC.

Coffee break location

Coffee breaks will be held in the only room on the 7th floor of tower B. Please note that the room is accessible only through the stairs of tower B.

Suggested Hotels

• Albergo Verdi | City centre | 20 minutes walk to the department
• Hotel Giotto | City centre | 20 minutes walk to the department
• NH Padova | Fair area | 10 minutes walk to the department
• Best Western | Fair area | 10 minutes walk to the department
• Hotel Igea | Hospital area | 15 minutes walk to the department

Food near Torre Archimede

• Panetteria Matiello | Gourmet panini takeaway | €
• Bar ACI | Panini and light lunch | €€
• Caffè Gozzi | Light lunch | €€
• Pizzeria Porteo | Mainly pizza | €€
• Handa | Fusion | €€
• Osteria Sofia | Traditional, good selection of local wines | €€€
• Florital | Fish restaurant | €€€

For any request of information, please write to orgwdf@math.unipd.it