Samuel Mimram

Categories and λ-calculus

I am tutoring exercise sessions for the course of categories and λ-calculus, which is taught by Paul-André Melliès and is part of the the MPRI master. More meterial is available on the webpage of the course (and see here for the rooms).

2022-2023

  1. Cartesian categories (solution)
  2. Coproducts, pullbacks, monoids (solution)
  3. Adjunctions (solution)
  4. Computing in the λ-calculus
  5. Strong normalization of the λ-calculus (solution)
  6. Realizability (solution)
  7. Algebras (solution)
  8. Monads (solution)
  9. Graphs and the Yoneda lemma (solution)

2021-2022

  1. Isomorphismes et spans
  2. Products, coproducts, pullbacks, monomorphisms
  3. Adjunctions
  4. An alternative formulation of adjunctions
  5. Quantifiers as adjoints
  6. Computing in the λ-calculus
  7. Strong normalization of the λ-calculus
  8. Normalization by evaluation
  9. Realizability
  10. Algebras
  11. Distributive laws between monads
  12. Graphs and the Yoneda lemma

2020-2021

  1. Cartesian categories (solution)
  2. Coproducts, pullbacks, monoids (solution)
  3. Adjunctions (solution)
  4. An equivalent formulation of adjunctions
  5. Equalizers, epi-mono factorization, first-order logic
  6. Computing in the λ-calculus (solution)
  7. Normalizing in the λ-calculus (solution)
  8. Algebras (solution)
  9. Monads (solution)
  10. Algebras for a monad (solution)
  11. Graphs and the Yoneda lemma

2019-2020

  1. Pullbacks, monos, epis and subobjects
  2. Equalizers, epi-mono factorization, first-order logic
  3. An equivalent formulation of adjunctions
  4. λ-calculus: confluence, termination
  5. Distributivity laws between functors and monads, Grothendieck construction and set-theoretic colimits
  6. Algebras

2018-2019

  1. Cartesian categories
  2. Coproducts, pullbacks, monoids
  3. Adjunctions
  4. Monads
  5. λ-calculus: confluence, termination
  6. Algebras
  7. Algebras for a monad
  8. Distributive laws between monads

2017-2018

  1. Cartesian categories
  2. Adjunctions
  3. Graphs and the Yoneda lemma
  4. Monads and algebras
  5. Presheaves as cocompletion

2016-2017

  1. Cartesian categories
  2. Graphs and the Yoneda lemma
  3. Pullbacks, monos, epis and subobjects
  4. Equalizers, epi-mono factorization, first-order logic
  5. Algebras
  6. A reformulation of adjunctions
  7. Distributivity laws between monads – Grothendieck construction and set-theoretic colimits

2015-2016

  1. Cartesian categories
  2. Graphs, adjunctions, monads
  3. Algebras
  4. λ-calculus and cartesian closed categories
  5. Categories of presheaves and colimits

2014-2015

  1. Cartesian categories
  2. Graphs, adjunctions, monads
  3. λ-calculus
  4. Algebras
  5. Realizability
  6. Presheaf categories, (co)limits
  7. Presentations of monoidal categories

2013-2014

  1. λ-calculus
  2. Graphs, adjunctions, monads
  3. Adjunctions, monads
  4. Cartesian and monoidal categories
  5. Algebras
  6. Closed categories
  7. Limits, presheaf categories

2012-2013

  1. λ-calculus
  2. Graphs, adjunctions, monads
  3. Adjunctions, monads
  4. Rewriting
  5. Realizability
  6. Cartesian categories
  7. Monoidal theories
  8. Limits, presheaf categories

2011-2012

  1. Graphes, catégories cartésiennes
  2. Monades
  3. Réalisabilité
  4. Adjunctions and monads
  5. λ-calculus
  6. Cartesian closed categories
  7. Catégories compactes closes

2010-2011

  1. Catégories cartésiennes
  2. Adjonctions
  3. Adjunctions and monads
  4. λ-calculus
  5. Cartesian closed categories
  6. Semantics of fixpoint

2009-2010

  1. Monoïdes
  2. Adjonctions, monade de non-déterminisme
  3. Monades
  4. Catégories cartésiennes fermées
  5. Catégories monoïdales
  6. Catégories compactes closes
  7. Catégories monoïdales tracées
  8. Catégories monoïdales tracées
  9. Modèles fonctoriels
  10. Limites, présentations de catégories
  11. Présentations de catégories monoïdales
  12. Lois distributives, catégories de jeux