Mathematical Culture and Thought

Mathematical Culture and Thought

Theory of Categories; Object or Tool

Document Type : Survey

Authors
A. Jafari 1
S. Yassemi 2
1 Department of Mathematical Sciences, Sharif University of Technology, Iran
2 2School of Mathematics, Statistics and Computer Science, University of Tehran, Iran
10.30504/mct.2023.1265.1880
Abstract
How important is the theory of categories? From the early days of its creation
until today, this question has occupied the minds of mathematicians and different
answers have been provided: For some categories are merely a tool. For others, they
are a fundamental part of today’s mathematics. Generally, questions like these do not
have definite and absolute answers. At least for this particular question, the mathematics
community has not reached a common answer, and probably will never reach a
resolution. Our goal in writing this article is to discuss the origins and developments
of the theory of categories and also discuss its role in mathematics
Keywords
category theory
derived categories
triangulated categories
K-theory
differential graded categories

Subjects

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  • Receive Date 26 January 2022
  • Revise Date 18 April 2022
  • Accept Date 08 May 2022
  • Publish Date 21 January 2023