On Feb 21, 2010, at 8:13 AM, Nick Rudnick wrote:
Of course a basic point about language is that the association
between sounds and meanings is (for the most part) arbitrary.
I would rather like to say it is not strictly determined, as an
evolutionary tendence towards, say ergonomy, cannot be
A place in the hall of fame and thank you for mentioning clopen... ;-)
Just wanting to present open/closed as and example of improvable maths
terminology, I oversaw this even more evident defect in it and even
copied it into my improvement proposal, bordered/unbordered:
It is questionable
Richard O'Keefe wrote:
On Feb 19, 2010, at 2:48 PM, Nick Rudnick wrote:
Please tell me the aspect you feel uneasy with, and please give me
your opinion, whether (in case of accepting this) you would rather
choose to consider Human as referrer and Int as referee of the
opposite -- for I think
On 19 Feb 2010, at 00:52, Richard O'Keefe wrote:
Turning to the Wikipedia article, we find
The word kangaroo derives from the Guugu Yimidhirr word gangurru,
referring to a grey kangaroo
Thanks, particularly for giving the name of the native language. Hope
the Wikipedia article can be
On 19 Feb 2010, at 00:05, Nick Rudnick wrote:
Mathematicians though stick to their own concepts and definitions
individually. For example, I had conversations with one who calls
monads triads, and then one has to cope with that.
Yes. But isn't it also an enrichment by some way?
Yes, one
On 19 Feb 2010, at 00:55, Daniel Fischer wrote:
I'd always assumed ring was generalised from Z[n].
As in cyclic group, arrange the numbers in a ring like on a
clockface?
Maybe. As far as I know, the term ring (in the mathematical sense)
first
appears in chapter 9 - Die Zahlringe des
Am Freitag 19 Februar 2010 10:42:59 schrieb Hans Aberg:
On 19 Feb 2010, at 00:55, Daniel Fischer wrote:
I'd always assumed ring was generalised from Z[n].
As in cyclic group, arrange the numbers in a ring like on a
clockface?
Maybe. As far as I know, the term ring (in the mathematical
On 19 Feb 2010, at 12:12, Daniel Fischer wrote:
...As far as I know, the term ring (in the mathematical sense)
first
appears in chapter 9 - Die Zahlringe des Körpers - of Hilbert's Die
Theorie der algebraischen Zahlkörper. Unfortunately, Hilbert gives
no hint
why he chose that name (Dedekind,
Am Freitag 19 Februar 2010 01:49:05 schrieb Nick Rudnick:
Daniel Fischer wrote:
Am Donnerstag 18 Februar 2010 19:19:36 schrieb Nick Rudnick:
Hi Hans,
agreed, but, in my eyes, you directly point to the problem:
* doesn't this just delegate the problem to the topic of limit
Am Freitag 19 Februar 2010 02:48:59 schrieb Nick Rudnick:
Hi,
wow, a topic specific response, at last... But I wish you would be more
specific... ;-)
A *referrer* (object) refers to a *referee* (object) by a *reference*
(arrow).
Doesn't work for me. Not in Ens (sets, maps), Grp
As well as books and reading material online, nowadays you can also find
video lectures...for example, the following was at the top of Googling
category theory video:
http://golem.ph.utexas.edu/category/2007/09/the_catsters_on_youtube.html
Cheers,
Mike.
Nick Rudnick wrote:
I haven't seen
On Thu, Feb 18, 2010 at 04:27, Nick Rudnick wrote:
I haven't seen anybody mentioning «Joy of Cats» by Adámek, Herrlich
Strecker:
It is available online, and is very well-equipped with thorough
explanations, examples, exercises funny illustrations, I would say best of
university lecture
IM(H??)O, a really introductive book on category theory still is to be
written -- if category theory is really that fundamental (what I
believe, due to its lifting of restrictions usually implicit at
'orthodox maths'), than it should find a reflection in our every day's
common sense, shouldn't
On 18 Feb 2010, at 14:48, Nick Rudnick wrote:
* the definition of open/closed sets in topology with the boundary
elements of a closed set to considerable extent regardable as facing
to an «outside» (so that reversing these terms could even appear
more intuitive, or «bordered» instead of
Am Donnerstag 18 Februar 2010 14:48:08 schrieb Nick Rudnick:
even in Germany, where the
term «ring» seems to originate from, since at least a century nowbody
has the least idea it once had an alternative meaning «gang,band,group»,
Wrong. The term Ring is still in use with that meaning in
Hi Daniel,
;-)) agreed, but is the word «Ring» itself in use? The same about the
English language... de.wikipedia says:
« Die Namensgebung /Ring/ bezieht sich nicht auf etwas anschaulich
Ringförmiges, sondern auf einen organisierten Zusammenschluss von
Elementen zu einem Ganzen. Diese
Am Donnerstag 18 Februar 2010 17:10:08 schrieb Nick Rudnick:
Hi Daniel,
;-)) agreed, but is the word «Ring» itself in use?
Of course, many people wear rings on their fingers.
Oh - you meant in the sense of gang/group?
It still appears as part of the name of some groups as a word of its own,
On Thu, Feb 18, 2010 at 7:48 AM, Nick Rudnick joerg.rudn...@t-online.dewrote:
IM(H??)O, a really introductive book on category theory still is to be
written -- if category theory is really that fundamental (what I believe,
due to its lifting of restrictions usually implicit at 'orthodox
Hi Hans,
agreed, but, in my eyes, you directly point to the problem:
* doesn't this just delegate the problem to the topic of limit
operations, i.e., in how far is the term «closed» here more perspicuous?
* that's (for a very simple concept) the way that maths prescribes:
+ historical
Gregg Reynolds wrote:
On Thu, Feb 18, 2010 at 7:48 AM, Nick Rudnick
joerg.rudn...@t-online.de mailto:joerg.rudn...@t-online.de wrote:
IM(H??)O, a really introductive book on category theory still is
to be written -- if category theory is really that fundamental
(what I believe, due
- Forwarded Message -
From: Michael Matsko msmat...@comcast.net
To: Nick Rudnick joerg.rudn...@t-online.de
Sent: Thursday, February 18, 2010 2:16:18 PM GMT -05:00 US/Canada Eastern
Subject: Re: [Haskell-cafe] Category Theory woes
Gregg,
Topologically speaking, the border
Am Donnerstag 18 Februar 2010 19:19:36 schrieb Nick Rudnick:
Hi Hans,
agreed, but, in my eyes, you directly point to the problem:
* doesn't this just delegate the problem to the topic of limit
operations, i.e., in how far is the term «closed» here more perspicuous?
It's fairly natural in
Am Donnerstag 18 Februar 2010 19:55:31 schrieb Nick Rudnick:
Gregg Reynolds wrote:
On Thu, Feb 18, 2010 at 7:48 AM, Nick Rudnick
joerg.rudn...@t-online.de mailto:joerg.rudn...@t-online.de wrote:
IM(H??)O, a really introductive book on category theory still is
to be written -- if
Sent: Thursday, February 18, 2010 2:16:18 PM GMT -05:00 US/Canada Eastern
Subject: Re: [Haskell-cafe] Category Theory woes
Gregg,
Topologically speaking, the border of an open set is called the
boundary of the set. The boundary is defined as the closure of the
set minus the set itself
On Feb 18, 2010, at 10:19 AM, Nick Rudnick wrote:
Back to the case of open/closed, given we have an idea about sets --
we in most cases are able to derive the concept of two disjunct sets
facing each other ourselves, don't we? The only lore missing is just
a Bool: Which term fits which
On 18 Feb 2010, at 20:20, Daniel Fischer wrote:
+ definition backtracking: «A closure operation c is defined by the
property c(c(x)) = c(x).
Actually, that's incomplete, ...
That's right, it is just the idempotency relation.
...missing are
- c(x) contains x
- c(x) is minimal among the
On 18 Feb 2010, at 19:19, Nick Rudnick wrote:
agreed, but, in my eyes, you directly point to the problem:
* doesn't this just delegate the problem to the topic of limit
operations, i.e., in how far is the term «closed» here more
perspicuous?
* that's (for a very simple concept) the way
Am Donnerstag 18 Februar 2010 21:47:02 schrieb Hans Aberg:
On 18 Feb 2010, at 20:20, Daniel Fischer wrote:
+ definition backtracking: «A closure operation c is defined by the
property c(c(x)) = c(x).
Actually, that's incomplete, ...
That's right, it is just the idempotency relation.
On Thu, Feb 18, 2010 at 1:31 PM, Daniel Fischer daniel.is.fisc...@web.dewrote:
Am Donnerstag 18 Februar 2010 19:55:31 schrieb Nick Rudnick:
Gregg Reynolds wrote:
-- you agree with me it's far away from every day's common sense, even
for a hobby coder?? I mean, this is not «Head first
To: Michael Matsko msmat...@comcast.net
Cc: haskell-cafe@haskell.org
Sent: Thursday, February 18, 2010 3:15:49 PM GMT -05:00 US/Canada Eastern
Subject: Re: Fwd: [Haskell-cafe] Category Theory woes
Hi Mike,
so an open set does not contain elements constituting a border/boundary of it,
does
On 18 Feb 2010, at 22:06, Daniel Fischer wrote:
...missing are
- c(x) contains x
- c(x) is minimal among the sets containing x with y = c(y).
It suffices*) with a lattice L with relation = (inclusion in the
case
of sets) satifying
i. x = y implies c(x) = c(y)
ii. x = c(x) for all x in
...@comcast.net
Cc: haskell-cafe@haskell.org
Sent: Thursday, February 18, 2010 3:15:49 PM GMT -05:00 US/Canada Eastern
Subject: Re: Fwd: [Haskell-cafe] Category Theory woes
Hi Mike,
so an open set does not contain elements constituting a
border/boundary of it, does it?
But a closed set does
On Feb 18, 2010, at 1:28 PM, Hans Aberg wrote:
It is a powerful concept. I think of a function closure as what one
gets when adding all an expression binds to, though I'm not sure
that is why it is called a closure.
Its because a monadic morphism into the same type carrying around data
Hans Aberg wrote:
On 18 Feb 2010, at 19:19, Nick Rudnick wrote:
agreed, but, in my eyes, you directly point to the problem:
* doesn't this just delegate the problem to the topic of limit
operations, i.e., in how far is the term «closed» here more perspicuous?
* that's (for a very simple
Hi Alexander,
my actual posting was about rename refactoring category theory;
closed/open was just presented as an example for suboptimal terminology
in maths. But of course, bordered/unbordered would be extended by e.g.
«partially bordered» and the same holds.
Cheers,
Nick
Alexander
On 18 Feb 2010, at 23:02, Nick Rudnick wrote:
418 bytes in my file system... how many in my brain...? Is it
efficient, inevitable?
Yes, it is efficient conceptually. The idea of closed sets let to
topology, and in combination with abstractions of differential
geometry led to cohomology
Gregg Reynolds wrote:
On Thu, Feb 18, 2010 at 1:31 PM, Daniel Fischer
daniel.is.fisc...@web.de mailto:daniel.is.fisc...@web.de wrote:
Am Donnerstag 18 Februar 2010 19:55:31 schrieb Nick Rudnick:
Gregg Reynolds wrote:
-- you agree with me it's far away from every day's common
On Feb 18, 2010, at 2:08 PM, Nick Rudnick wrote:
my actual posting was about rename refactoring category theory;
closed/open was just presented as an example for suboptimal
terminology in maths. But of course, bordered/unbordered would be
extended by e.g. «partially bordered» and the same
GMT -05:00 US/Canada Eastern
Subject: Re: [Haskell-cafe] Category Theory woes
Hi Mike,
of course... But in the same spirit, one could introduce a straightforward
extension, «partially bordered», which would be as least as good as «clopen»...
;-)
I must admit we've come a little off
Hans Aberg wrote:
On 18 Feb 2010, at 23:02, Nick Rudnick wrote:
418 bytes in my file system... how many in my brain...? Is it
efficient, inevitable?
Yes, it is efficient conceptually. The idea of closed sets let to
topology, and in combination with abstractions of differential
geometry led
On Feb 19, 2010, at 3:55 AM, Daniel Fischer wrote:
Am Donnerstag 18 Februar 2010 14:48:08 schrieb Nick Rudnick:
even in Germany, where the
term «ring» seems to originate from, since at least a century nowbody
has the least idea it once had an alternative meaning
«gang,band,group»,
Wrong.
Alexander Solla wrote:
On Feb 18, 2010, at 2:08 PM, Nick Rudnick wrote:
my actual posting was about rename refactoring category theory;
closed/open was just presented as an example for suboptimal
terminology in maths. But of course, bordered/unbordered would be
extended by e.g. «partially
On Feb 19, 2010, at 11:22 AM, Hans Aberg wrote:
As for the naming problem, it is more of a linguistic problem: the
names were somehow handed by tradition, and it may be difficult to
change them. For example, there is a rumor that kangaroo means I
do not understand in a native language;
Am Freitag 19 Februar 2010 00:24:23 schrieb Richard O'Keefe:
On Feb 19, 2010, at 3:55 AM, Daniel Fischer wrote:
Am Donnerstag 18 Februar 2010 14:48:08 schrieb Nick Rudnick:
even in Germany, where the
term «ring» seems to originate from, since at least a century nowbody
has the least idea
Daniel Fischer wrote:
Am Donnerstag 18 Februar 2010 19:19:36 schrieb Nick Rudnick:
Hi Hans,
agreed, but, in my eyes, you directly point to the problem:
* doesn't this just delegate the problem to the topic of limit
operations, i.e., in how far is the term «closed» here more perspicuous?
On Feb 18, 2010, at 4:49 PM, Nick Rudnick wrote:
Why does the opposite work well for computing science?
Does it? I remember a peer trying to convince me to use the factory
pattern in a language that supports functors. I told him I would do
my task my way, and he could change it later
Hi Alexander,
please be more specific -- what is your proposal?
Seems as if you had more to say...
Nick
Alexander Solla wrote:
On Feb 18, 2010, at 4:49 PM, Nick Rudnick wrote:
Why does the opposite work well for computing science?
Does it? I remember a peer trying to convince me to
Hi,
wow, a topic specific response, at last... But I wish you would be more
specific... ;-)
A *referrer* (object) refers to a *referee* (object) by a *reference*
(arrow).
Doesn't work for me. Not in Ens (sets, maps), Grp (groups, homomorphisms),
Top (topological spaces, continuous
On Feb 19, 2010, at 2:48 PM, Nick Rudnick wrote:
Please tell me the aspect you feel uneasy with, and please give me
your opinion, whether (in case of accepting this) you would rather
choose to consider Human as referrer and Int as referee of the
opposite -- for I think this is a deep
I haven't seen anybody mentioning «Joy of Cats» by Adámek, Herrlich
Strecker:
It is available online, and is very well-equipped with thorough
explanations, examples, exercises funny illustrations, I would say
best of university lecture style: http://katmat.math.uni-bremen.de/acc/.
On Tue, Feb 2, 2010 at 5:26 AM, Mark Spezzano
mark.spezz...@chariot.net.auwrote:
Hi all,
Has anyone else found it frustratingly difficult to find details on
easy-to-diget material on Category theory. The Chapter that I'm stuck on is
actually labeled Preliminaries and so I reason that if I
On Feb 16, 2010, at 9:43 AM, Gregg Reynolds wrote:
I've looked through at least a dozen. For neophytes, the best of
the bunch BY FAR is Goldblatt, Topoi: the categorial analysis of
logic . Don't be put off by the title. He not only explains the
stuff, but he explains the problems that
Hi all,
I'm trying to learn Haskell and have come across Monads. I kind of understand
monads now, but I would really like to understand where they come from. So I
got a copy of Barr and Well's Category Theory for Computing Science Third
Edition, but the book has really left me dumbfounded.
I should probably add that I am trying various proofs that involve injective
and surjective properties of Hom Sets and Hom functions.
Does anyone know what Hom stands for?
I need a text for a newbie.
Mark
On 02/02/2010, at 9:56 PM, Mark Spezzano wrote:
Hi all,
I'm trying to learn Haskell
Hom(A, B) is just a set of morphisms from A to B.
Mark Spezzano wrote:
I should probably add that I am trying various proofs that involve injective
and surjective properties of Hom Sets and Hom functions.
Does anyone know what Hom stands for?
I need a text for a newbie.
Mark
On 02/02/2010,
You may try Pierce's Basic Category Theory for Computer Scientists or
Awodey's Category Theory, whose style is rather introductory. Both of them
(I think) have a chapter about functors where they explain the Hom functor
and related topics.
Alvaro.
2010/2/2 Mark Spezzano
Mark Spezzano wrote:
I need a text for a newbie.
While the other books suggested are excellent, I think that they would
be hard going if you find Barr Wells difficult.
The simplest introduction to the ideas of category theory that I know is
Conceptual Mathematics by F W Lawvere S H
2010/2/2 Álvaro García Pérez agar...@babel.ls.fi.upm.es
You may try Pierce's Basic Category Theory for Computer Scientists or
Awodey's Category Theory, whose style is rather introductory. Both of them
(I think) have a chapter about functors where they explain the Hom functor
and related
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