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Questions tagged [category-theory]

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9 votes
1 answer

Did Ulam discover category theory?

(The following query by Noam Zeilberger has recently appeared on the Categories mailing list; I am taking the liberty of asking it here.) In Ulam's autobiography Adventures of a Mathematician, there ...
1 vote
0 answers

Was there historical influence of lattice theory on category theory?

I know that Maclane and Eilenberg created category theory together. And I also know that lattice theory is a concept created by Dedekind with the motivation of ring and ideal theory. And this concept ...
2 votes
0 answers

The origin of $∂^2=0$ and $d^2=0$

I know that formula $∂^2=0$ and $d^2=0$ very important in the homology and cohomology theory. And I understand that this formula was generated from the process of finding a solution to the partial ...
2 votes
0 answers

How did Grothendieck come in contact with Category theory?

Category theory was formalized around 1950s, and Grothendieck made his breakthrough papers about 10-20 years from that time. I wish to know, how was it possible the ideas of Category Theory were so ...
10 votes
3 answers

Philosophy behind category theory

Category theory represented a huge change in the way the community thought about mathematics, leaving its the set theoretic nature behind and bringing up the importance of arrows between the objects ...
2 votes
0 answers

The first commutative diagram

Cf. Is this the first ever commutative diagram? By commutative diagram I mean anything that shows an equality (or ...
15 votes
3 answers

How did Grothendieck encounter and adopt the categorical language?

Apparently the first mathematical publication of Grothendieck where he uses the terms “functor” and “category” in the technical sense is the Kansas report. From where Grothendieck had knowledge of ...
-1 votes
1 answer

How long have all the mathematicians working in the respective fields known the theory of categories

Vague the question: how long have all the mathematicians working in the respective fields known the theory of categories? More specific questions: Is it true that all modern working algebraic ...
5 votes
1 answer

Where did the notion of the product in a category first appear?

In his book, Category Theory[1], Awodey writes the following about it: Next, we are going to see the categorical definition of a product of two objects in a category. This was first given by Mac Lane ...
32 votes
1 answer

Was object oriented programming influenced by the mathematical category theory?

Object oriented programming (OOP) is a programming model where code and data are encapsulated into units called objects that behave semi-autonomously. Interaction between objects is arranged through ...