16
votes
Accepted
How did Grothendieck encounter and adopt the categorical language?
Grothendieck's familiarity with the categories predates Kansas. In 1948-1949 he attended Séminaire Cartan at École Normale Supérieure, where he "took the liberty of speaking to Cartan, as if to ...
- 78.3k
15
votes
Why are the categories of category theory called "category"?
Here is Saunders Mac Lane's own explanation of why he and Eilenberg chose the words "category", "functor" and "natural transformation":
A direct treatment of categories ...
- 471
12
votes
Why are the categories of category theory called "category"?
It will probably be difficult to find documentation of Eilenberg and Mac Lane's thinking (added later - perhaps not as difficult as I thought!), but I would argue that a category does, in fact, ...
- 221
10
votes
Did Ulam discover category theory?
Not discovered, but Ulam might have anticipated some aspects of category theory and possibly influenced Eilenberg. Kuratowski's comment on Ulam's 1932 Master's thesis reads:"The work is a study ...
- 78.3k
6
votes
Philosophy behind category theory
The conventional view is that categories were introduced by Samuel Eilenberg and Saunders Mac Lane in the 1940s as a tool for the study of algebraic topology. What we now call functors and natural ...
- 1,546
4
votes
Accepted
Where did the notion of the product in a category first appear?
It appears in MacLane's 1950 paper Duality for Groups, published in the Bulletin of AMS. Of course, he is dealing specifically with the category of groups, but the definition is categorical. Section 3,...
- 78.3k
3
votes
How did Grothendieck encounter and adopt the categorical language?
In the "Esquisse Thématique des Principaux Travaux Mathématique 4.a Algèbre catégorique", Grothendieck says:
En fait, de facon continuelle depuis 1953, je me suis senti dans l'obligation, ...
- 402
3
votes
Philosophy behind category theory
It's only a 'huge' change because set theory formalities, aka ZFC, was so hegemonic.
Had a wider discussion ensued as to what to take as axiomatic, the function or the set or both, then the sea change ...
- 3,788
3
votes
Why are the categories of category theory called "category"?
According to Mathword
The term category was introduced by Samuel Eilenberg; Saunders MacLane "General Theory of Natural Equivalences," Transactions of the American Mathematical Society, Vol....
- 10.5k
2
votes
How long have all the mathematicians working in the respective fields known the theory of categories
I am an algebraist. In the first edition of Lang's "Algebra", category theory was called "abstract nonsense". I bought the book 47 years ago. That is how long I know it. It is ...
2
votes
Why are the categories of category theory called "category"?
In addition to the form extressed by Mac Lane in his Categories for the Working Mathematician (1971) as pointed out by Baez there is a similar later explanation found in:
Mac Lane, S. (1996). The ...
- 1,761
1
vote
Why are the categories of category theory called "category"?
According to the Stanford Encyclopedia of Philosophy (emphasis mine):
Categories, functors, natural transformations, limits and colimits appeared almost out of nowhere in a paper by Eilenberg & ...
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