MATHEMATICS: FROM SET THEORY TO CATEGORY THEORY
- Authors: Serovaisky S.Y.1
-
Affiliations:
- Al-Farabi Kazakh National University
- Issue: No 1 (2022)
- Pages: 29-34
- Section: GENESIS OF PROGRAMMES IN METAPHYSICS AND MATHEMATICS
- URL: https://macrosociolingusictics.ru/metaphysics/article/view/30764
- DOI: https://doi.org/10.22363/2224-7580-2022-1-29-34
Cite item
Full Text
Abstract
The basis of mathematics is set theory, to which almost all mathematical directions go back. However, the importance of category theory for mathematics as a whole is steadily increasing. If in set theory the determining role is played by the internal structure of the object under consideration, then in category theory an object is characterized by its connections with other objects. The article discusses the features of set-theoretic and category-theoretic approaches in mathematics.
Keywords
About the authors
S. Ya Serovaisky
Al-Farabi Kazakh National University
Email: serovajskys@mail.ru
71 al-Farabi Ave, Almaty, 050040, Kazakhstan
References
- Бурбаки Н. Теория множеств. М.: Мир, 1965.
- Букур И., Деляну А. Введение в теорию категорий и функторов. М.: Мир, 1972.
- Голдблатт Р. Топосы. Категорный анализ логики. М.: Мир, 1983.
- Иванов И. Нужна ли физикам теория категорий? URL: https://elementy.ru/ novosti_nauki/430819.
- Rydeheard D.E., Burstall R.M. Computational Category Theory. New York: Prentice Hall, 1988.
- Serovajsky S. Architecture of Mathematics. London: Chapman and Hall/CRC, 2020.
