| 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?)
- : Category Theory
- : Conceptual Mathematics
- : Topoi: the Categorial Analysis of Logic
Auxiliar
- : Arrows, Structures, Functors: the Categorical Imperative
- : Category Theory for Computing Science
- : Sets for Mathematics
- : Basic Category Theory for Computer Scientists
- : Handbook of Categorical Algebra
- : Abstract and Concrete Categories: the Joy of Cats
- : Categories for the Working Mathematician
Links
Hints
- : «How to write mathematics badly» (video lecture)
- : How to write mathematics
- : Mathematical writing
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