2018.1 🐈 Category theory

Schedule:6T56 [16h50–18h30]
Classroom:A225
Contact:thanos@imd.ufrn.br

Prerequisites

  • required:
    • mathematical maturity: you should be able to reason and to express mathematical ideas in natural language;
    • familiarity with mathematical logic and set theory;
    • familiarity with the general ideas and tools of abstract algebra;
  • obvious:
    • {will, time} to {pratice, study, research}

Syllabus

Categories: definitions and examples. Commutative diagrams. Definitions using arrows. Languages of functional programming as categories. Constructions in categories. Universal constructions. Epis and monos. Duality principle. Products and coproducts. Equalizers and coequalizers. Limits and colimits. Functors. Deduction systems as categories. Exponentials. CCC (Cartesian closed categories) and lambda calculus. Natural transformations. Yoneda lemma. Adjunction. Monads.

Bibliography

Main

(Heard of libgen.io?)

  • Awodey: Category Theory
  • Lawvere & Schanuel: Conceptual Mathematics
  • Goldblatt: Topoi: the Categorial Analysis of Logic

Auxiliar

Links

Hints

Exams

No information regarding exams for the time being.

History log

02/03/2018

  • First meeting; introduction

16/03/2018

  • Arbib & Manes, Ch. 1

23/03/2018

  • Arbib & Manes, Ch. 2

20/04/2018

  • Awodey, Ch. 1

27/04/2018

  • Awodey, Ch. 1

04/05/2018

  • Awodey, Ch. 2

11/05/2018

  • Awodey, Ch. 2

18/05/2018

  • Awodey, Ch. 3

25/05/2018

  • Awodey, Ch. 3

01/06/2018

  • Awodey, Ch. 4

08/06/2018

  • Awodey, Ch. 4

15/06/2018

  • Awodey, Ch. 5

22/06/2018

  • Awodey, Ch. 5

29/06/2018

  • Awodey, Ch. 7

06/07/2018

  • Awodey, Ch. 7

Last update: Fri Jul 20 22:46:56 -03 2018