When do triples have been called monads for the first time?When does the 2-category V-Cat have pseudo-pullbacks? When did the term “Lie group” first appear?When has pure mathematics been influenced by the social context of mathematicians?Historical questions on the term “general abstract nonsense”When was the “arrow notation” for functions first introduced?When and what was the first proof $mathbbQ$ is countable?Where did Zermelo first model the natural numbers by iterates of the singleton operator, and have the definitions been compared by himself?What parts of the theory of quasicategories have been simplified since the publication of HTT?
When do triples have been called monads for the first time?
When does the 2-category V-Cat have pseudo-pullbacks? When did the term “Lie group” first appear?When has pure mathematics been influenced by the social context of mathematicians?Historical questions on the term “general abstract nonsense”When was the “arrow notation” for functions first introduced?When and what was the first proof $mathbbQ$ is countable?Where did Zermelo first model the natural numbers by iterates of the singleton operator, and have the definitions been compared by himself?What parts of the theory of quasicategories have been simplified since the publication of HTT?
$begingroup$
I am fine-tuning a short note on basic category theory; any such course must introduce monads, and I want to give a bit of history of the subject.
I soon realized that I don't know the precise series of events that led Mac Lane to create the name "monad" (but it was him who coined the term, or he simply advertized it?) instead of the way less creative "triple" or "standard construction".
The only reference I can find is a broken link at the nLab page.
ct.category-theory ho.history-overview
asked 8 hours ago
FoscoFosco
4,8131 gold badge20 silver badges45 bronze badges
$endgroup$
add a comment |
$begingroup$
I am fine-tuning a short note on basic category theory; any such course must introduce monads, and I want to give a bit of history of the subject.
I soon realized that I don't know the precise series of events that led Mac Lane to create the name "monad" (but it was him who coined the term, or he simply advertized it?) instead of the way less creative "triple" or "standard construction".
The only reference I can find is a broken link at the nLab page.
ct.category-theory ho.history-overview
asked 8 hours ago
FoscoFosco
4,8131 gold badge20 silver badges45 bronze badges
$endgroup$
$begingroup$
Surely a kind of back-formation from monoid? Coupled perhaps with the love of purloining terms from philosophy. I don't know that it needed more than one event, namely the recognition that a monad is a monoid in a category of endofunctors, like his book says.
$endgroup$
– Todd Trimble♦
8 hours ago
$begingroup$
see also stackoverflow.com/q/3870088 (with an answer that has 754 upvotes...)
$endgroup$
– Carlo Beenakker
8 hours ago
$begingroup$
My guess about the broken link is that it is to the email of Ross Street to the categories mailing list (dated 03 Nov 2007) starting with the sentence "History can be harder than mathematics.", available from mta.ca/~cat-dist/archive/2007/07-11 There was a lot of discussion about history in that email thread, and not 100% agreement on events from the 1960s (CT had a poor publication record at the time, due to the lack of dedicated journals, so results percolated via conference proceedings/abstracts, discussions etc. I think few people saw it then as a field of research)
$endgroup$
– David Roberts
3 hours ago
add a comment |
$begingroup$
I am fine-tuning a short note on basic category theory; any such course must introduce monads, and I want to give a bit of history of the subject.
I soon realized that I don't know the precise series of events that led Mac Lane to create the name "monad" (but it was him who coined the term, or he simply advertized it?) instead of the way less creative "triple" or "standard construction".
The only reference I can find is a broken link at the nLab page.
ct.category-theory ho.history-overview
asked 8 hours ago
FoscoFosco
4,8131 gold badge20 silver badges45 bronze badges
$endgroup$
I am fine-tuning a short note on basic category theory; any such course must introduce monads, and I want to give a bit of history of the subject.
I soon realized that I don't know the precise series of events that led Mac Lane to create the name "monad" (but it was him who coined the term, or he simply advertized it?) instead of the way less creative "triple" or "standard construction".
The only reference I can find is a broken link at the nLab page.
ct.category-theory ho.history-overview
ct.category-theory ho.history-overview
asked 8 hours ago
FoscoFosco
4,8131 gold badge20 silver badges45 bronze badges
asked 8 hours ago
FoscoFosco
4,8131 gold badge20 silver badges45 bronze badges
edited 8 hours ago
Fosco
asked 8 hours ago
FoscoFosco
4,8131 gold badge20 silver badges45 bronze badges
asked 8 hours ago
FoscoFosco
4,8131 gold badge20 silver badges45 bronze badges
asked 8 hours ago
FoscoFosco
4,8131 gold badge20 silver badges45 bronze badges
4,8131 gold badge20 silver badges45 bronze badges
$begingroup$
Surely a kind of back-formation from monoid? Coupled perhaps with the love of purloining terms from philosophy. I don't know that it needed more than one event, namely the recognition that a monad is a monoid in a category of endofunctors, like his book says.
$endgroup$
– Todd Trimble♦
8 hours ago
$begingroup$
see also stackoverflow.com/q/3870088 (with an answer that has 754 upvotes...)
$endgroup$
– Carlo Beenakker
8 hours ago
$begingroup$
My guess about the broken link is that it is to the email of Ross Street to the categories mailing list (dated 03 Nov 2007) starting with the sentence "History can be harder than mathematics.", available from mta.ca/~cat-dist/archive/2007/07-11 There was a lot of discussion about history in that email thread, and not 100% agreement on events from the 1960s (CT had a poor publication record at the time, due to the lack of dedicated journals, so results percolated via conference proceedings/abstracts, discussions etc. I think few people saw it then as a field of research)
$endgroup$
– David Roberts
3 hours ago
add a comment |
$begingroup$
Surely a kind of back-formation from monoid? Coupled perhaps with the love of purloining terms from philosophy. I don't know that it needed more than one event, namely the recognition that a monad is a monoid in a category of endofunctors, like his book says.
$endgroup$
– Todd Trimble♦
8 hours ago
$begingroup$
see also stackoverflow.com/q/3870088 (with an answer that has 754 upvotes...)
$endgroup$
– Carlo Beenakker
8 hours ago
$begingroup$
My guess about the broken link is that it is to the email of Ross Street to the categories mailing list (dated 03 Nov 2007) starting with the sentence "History can be harder than mathematics.", available from mta.ca/~cat-dist/archive/2007/07-11 There was a lot of discussion about history in that email thread, and not 100% agreement on events from the 1960s (CT had a poor publication record at the time, due to the lack of dedicated journals, so results percolated via conference proceedings/abstracts, discussions etc. I think few people saw it then as a field of research)
$endgroup$
– David Roberts
3 hours ago
$begingroup$
Surely a kind of back-formation from monoid? Coupled perhaps with the love of purloining terms from philosophy. I don't know that it needed more than one event, namely the recognition that a monad is a monoid in a category of endofunctors, like his book says.
$endgroup$
– Todd Trimble♦
8 hours ago
$begingroup$
Surely a kind of back-formation from monoid? Coupled perhaps with the love of purloining terms from philosophy. I don't know that it needed more than one event, namely the recognition that a monad is a monoid in a category of endofunctors, like his book says.
$endgroup$
– Todd Trimble♦
8 hours ago
$begingroup$
see also stackoverflow.com/q/3870088 (with an answer that has 754 upvotes...)
$endgroup$
– Carlo Beenakker
8 hours ago
$begingroup$
see also stackoverflow.com/q/3870088 (with an answer that has 754 upvotes...)
$endgroup$
– Carlo Beenakker
8 hours ago
$begingroup$
My guess about the broken link is that it is to the email of Ross Street to the categories mailing list (dated 03 Nov 2007) starting with the sentence "History can be harder than mathematics.", available from mta.ca/~cat-dist/archive/2007/07-11 There was a lot of discussion about history in that email thread, and not 100% agreement on events from the 1960s (CT had a poor publication record at the time, due to the lack of dedicated journals, so results percolated via conference proceedings/abstracts, discussions etc. I think few people saw it then as a field of research)
$endgroup$
– David Roberts
3 hours ago
$begingroup$
My guess about the broken link is that it is to the email of Ross Street to the categories mailing list (dated 03 Nov 2007) starting with the sentence "History can be harder than mathematics.", available from mta.ca/~cat-dist/archive/2007/07-11 There was a lot of discussion about history in that email thread, and not 100% agreement on events from the 1960s (CT had a poor publication record at the time, due to the lack of dedicated journals, so results percolated via conference proceedings/abstracts, discussions etc. I think few people saw it then as a field of research)
$endgroup$
– David Roberts
3 hours ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
P. T. Johnstone (who wrote several books on Topos Theory) gave a Category Theory lecture in which he said this was originally called 'the standard construction', then 'triples', and finally 'monads' -- but he provided the caveat that mathematicians in Montreal still adhere to the term 'triples', such that if you're in Montreal and want to discuss monads, you should probably bear this in mind.
answered 8 hours ago
Adam P. GoucherAdam P. Goucher
7,2852 gold badges32 silver badges63 bronze badges
$endgroup$
$begingroup$
I'll bear this in mind if I go to Montreal.
$endgroup$
– Fosco
8 hours ago
2
$begingroup$
Notably Barr. (I'm not aware that everyone else is or was adamant about it, and I lived there for six months.) Added later: Joyal says "monad"; I've never heard him say "triple".
$endgroup$
– Todd Trimble♦
7 hours ago
add a comment |
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1 Answer
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1 Answer
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$begingroup$
P. T. Johnstone (who wrote several books on Topos Theory) gave a Category Theory lecture in which he said this was originally called 'the standard construction', then 'triples', and finally 'monads' -- but he provided the caveat that mathematicians in Montreal still adhere to the term 'triples', such that if you're in Montreal and want to discuss monads, you should probably bear this in mind.
answered 8 hours ago
Adam P. GoucherAdam P. Goucher
7,2852 gold badges32 silver badges63 bronze badges
$endgroup$
$begingroup$
I'll bear this in mind if I go to Montreal.
$endgroup$
– Fosco
8 hours ago
2
$begingroup$
Notably Barr. (I'm not aware that everyone else is or was adamant about it, and I lived there for six months.) Added later: Joyal says "monad"; I've never heard him say "triple".
$endgroup$
– Todd Trimble♦
7 hours ago
add a comment |
$begingroup$
P. T. Johnstone (who wrote several books on Topos Theory) gave a Category Theory lecture in which he said this was originally called 'the standard construction', then 'triples', and finally 'monads' -- but he provided the caveat that mathematicians in Montreal still adhere to the term 'triples', such that if you're in Montreal and want to discuss monads, you should probably bear this in mind.
answered 8 hours ago
Adam P. GoucherAdam P. Goucher
7,2852 gold badges32 silver badges63 bronze badges
$endgroup$
$begingroup$
I'll bear this in mind if I go to Montreal.
$endgroup$
– Fosco
8 hours ago
2
$begingroup$
Notably Barr. (I'm not aware that everyone else is or was adamant about it, and I lived there for six months.) Added later: Joyal says "monad"; I've never heard him say "triple".
$endgroup$
– Todd Trimble♦
7 hours ago
add a comment |
$begingroup$
P. T. Johnstone (who wrote several books on Topos Theory) gave a Category Theory lecture in which he said this was originally called 'the standard construction', then 'triples', and finally 'monads' -- but he provided the caveat that mathematicians in Montreal still adhere to the term 'triples', such that if you're in Montreal and want to discuss monads, you should probably bear this in mind.
answered 8 hours ago
Adam P. GoucherAdam P. Goucher
7,2852 gold badges32 silver badges63 bronze badges
$endgroup$
P. T. Johnstone (who wrote several books on Topos Theory) gave a Category Theory lecture in which he said this was originally called 'the standard construction', then 'triples', and finally 'monads' -- but he provided the caveat that mathematicians in Montreal still adhere to the term 'triples', such that if you're in Montreal and want to discuss monads, you should probably bear this in mind.
answered 8 hours ago
Adam P. GoucherAdam P. Goucher
7,2852 gold badges32 silver badges63 bronze badges
answered 8 hours ago
Adam P. GoucherAdam P. Goucher
7,2852 gold badges32 silver badges63 bronze badges
answered 8 hours ago
Adam P. GoucherAdam P. Goucher
7,2852 gold badges32 silver badges63 bronze badges
answered 8 hours ago
Adam P. GoucherAdam P. Goucher
7,2852 gold badges32 silver badges63 bronze badges
7,2852 gold badges32 silver badges63 bronze badges
$begingroup$
I'll bear this in mind if I go to Montreal.
$endgroup$
– Fosco
8 hours ago
2
$begingroup$
Notably Barr. (I'm not aware that everyone else is or was adamant about it, and I lived there for six months.) Added later: Joyal says "monad"; I've never heard him say "triple".
$endgroup$
– Todd Trimble♦
7 hours ago
add a comment |
$begingroup$
I'll bear this in mind if I go to Montreal.
$endgroup$
– Fosco
8 hours ago
2
$begingroup$
Notably Barr. (I'm not aware that everyone else is or was adamant about it, and I lived there for six months.) Added later: Joyal says "monad"; I've never heard him say "triple".
$endgroup$
– Todd Trimble♦
7 hours ago
$begingroup$
I'll bear this in mind if I go to Montreal.
$endgroup$
– Fosco
8 hours ago
$begingroup$
I'll bear this in mind if I go to Montreal.
$endgroup$
– Fosco
8 hours ago
2
2
$begingroup$
Notably Barr. (I'm not aware that everyone else is or was adamant about it, and I lived there for six months.) Added later: Joyal says "monad"; I've never heard him say "triple".
$endgroup$
– Todd Trimble♦
7 hours ago
$begingroup$
Notably Barr. (I'm not aware that everyone else is or was adamant about it, and I lived there for six months.) Added later: Joyal says "monad"; I've never heard him say "triple".
$endgroup$
– Todd Trimble♦
7 hours ago
add a comment |
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$begingroup$
Surely a kind of back-formation from monoid? Coupled perhaps with the love of purloining terms from philosophy. I don't know that it needed more than one event, namely the recognition that a monad is a monoid in a category of endofunctors, like his book says.
$endgroup$
– Todd Trimble♦
8 hours ago
$begingroup$
see also stackoverflow.com/q/3870088 (with an answer that has 754 upvotes...)
$endgroup$
– Carlo Beenakker
8 hours ago
$begingroup$
My guess about the broken link is that it is to the email of Ross Street to the categories mailing list (dated 03 Nov 2007) starting with the sentence "History can be harder than mathematics.", available from mta.ca/~cat-dist/archive/2007/07-11 There was a lot of discussion about history in that email thread, and not 100% agreement on events from the 1960s (CT had a poor publication record at the time, due to the lack of dedicated journals, so results percolated via conference proceedings/abstracts, discussions etc. I think few people saw it then as a field of research)
$endgroup$
– David Roberts
3 hours ago