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From: Marta Bunge <marta.bunge@mcgill.ca>
To: <categories@mta.ca>
Subject: RE: property_vs_structure
Date: Sat, 9 Oct 2010 18:26:10 -0400	[thread overview]
Message-ID: <E1P4iB9-000092-EF@mlist.mta.ca> (raw)
In-Reply-To: <20101009210755.68229A98F@mailscan2.ncs.mcgill.ca>

Dear Eduardo,>In a  previous message of mine and  in response to your  questions >
>> What do we mean by structure ?, and, what do we mean by property  ?
>
 I wrote>
>> On a given data, a structure is additional data on it such that, if it exists, it is not necessarily unique up to isomorphism. >>A property is additional data such that, if it exists, it is unique up to isomorphism (in the model theoretic sense).>
to which you replied>  
>> Well, here it is necessary first to establish what do we mean by 
>> "isomorphism". To do this we need a way to compare the structures, that is, we 
>> have to define morphism of structures (see below). Without this, the above is 
>> meaningless.>
Notice that I specified "in the model theoretic sense". In that context, the notions of a structure and of a morphism of structures are defined and it is that sense that I meant them. They are perfectly meaningful. 
>
You added> 
>> People discussing structure vs property were giving examples where all this 
>> was clear and straightforward (invertibility in a monoid, neutral element in a 
>> semigroup, etc). My original purpose when I wrote my first mail was to 
>> consider a less trivial example testing the following "definitions", that I 
>> see you subscribe above at least in what it concerns "structure" and "property":
> 
> *********
> Michael Shulman wrote:
>> (**)
>> property = forgetful functor is full and faithful
>> structure = forgetful functor is faithful
>> property-like structure = forgetful functor is pseudomonic
> **********
>
I do not "subscribe" to these notions. I simply use the well-known notions from first-order logic and model theory as I said earlier. I am aware of the difference between the locally connected  and the general case concerning covering projections and it is not the mathematics that I was disputing.  But I still have trouble following your analysis of this situation as was your purpose. The difference is that, whereas you consider the notion of a covering projection to be a property of a continuous map p from X to B which, in the general (non locally connected case) is a "hidden structure", I view the notion of a covering projection to be a structure in the first place and, in the specific locally connected case, one that may be equivalently reduced to a property. Every property is a structure, but not  every structure is  reducible to a property. 

>
All the best,  Marta



  		 	   		  

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  parent reply	other threads:[~2010-10-09 22:26 UTC|newest]

Thread overview: 33+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2010-09-23 10:07 The omega-functor omega-category David Leduc
2010-09-24 15:13 ` Urs Schreiber
2010-09-25  1:40   ` Ross Street
     [not found] ` <BF755983-D6D4-469B-9206-C6B275699C3F@mq.edu.au>
2010-09-25 11:22   ` Urs Schreiber
2010-09-26  2:00     ` David Leduc
     [not found] ` <1216D94C-81A2-49A7-95B3-7543B315A54B@mq.edu.au>
2010-09-26  5:00   ` David Leduc
     [not found] ` <E1P0Oe6-0005AL-SX@mlist.mta.ca>
2010-09-28  1:11   ` David Leduc
2010-09-29  1:09     ` John Baez
2010-09-30  0:29       ` David Leduc
     [not found] ` <AANLkTi=LXzu13GU8ZmB=+-qGTQmV3S-bDp6h+dJJ1xNJ@mail.gmail.com>
2010-09-30  3:10   ` John Baez
2010-10-01 14:22     ` Steve Vickers
2010-10-02 22:03       ` Michael Shulman
2010-10-03 13:32         ` Colin McLarty
2010-10-04  7:52         ` Vaughan Pratt
2010-10-04 18:41           ` Michael Shulman
2010-10-05 15:42             ` property_vs_structure Eduardo J. Dubuc
2010-10-06 12:34               ` errata Eduardo J. Dubuc
     [not found] ` <AANLkTin3LqPLuMFD-xSEuRK9TqBUbHrRRxrdcOEykJJo@mail.gmail.com>
2010-10-03 22:11   ` The omega-functor omega-category Michael Shulman
     [not found] ` <20101007010252.EA0FDCF26@mailscan2.ncs.mcgill.ca>
2010-10-07 23:46   ` errata Marta Bunge
     [not found]   ` <SNT101-W63B3FACD04EBDB79A3E389DF6F0@phx.gbl>
2010-10-08  0:40     ` property_vs_structure Eduardo J. Dubuc
     [not found] ` <20101008004112.BE2B38572@mailscan2.ncs.mcgill.ca>
2010-10-08 19:19   ` property_vs_structure Marta Bunge
     [not found]   ` <SNT101-W2444EC2F259963200F4CEEDF500@phx.gbl>
2010-10-08 21:53     ` property_vs_structure Eduardo J. Dubuc
     [not found]     ` <20101008215343.9920DABC2@mailscan2.ncs.mcgill.ca>
     [not found]       ` <SNT101-W455AA430BC53CBFDB8DCE3DF510@phx.gbl>
2010-10-09 14:12         ` FW: property_vs_structure Marta Bunge
2010-10-09 21:07         ` property_vs_structure Eduardo J. Dubuc
2010-10-11 13:03           ` property_vs_structure George Janelidze
     [not found] ` <20101009210755.68229A98F@mailscan2.ncs.mcgill.ca>
2010-10-09 22:26   ` Marta Bunge [this message]
     [not found] ` <20101011201507.3A7732E52@mailscan3.ncs.mcgill.ca>
2010-10-18 21:04   ` property_vs_structure Marta Bunge
2010-10-21  0:14     ` property_vs_structure George Janelidze
2010-10-21 17:51 ` property_vs_structure Marta Bunge
     [not found] ` <20101021002656.76CCDD13F@mailscan3.ncs.mcgill.ca>
2010-10-24 21:15   ` property_vs_structure Marta Bunge
2010-10-25 11:15     ` property_vs_structure George Janelidze
     [not found] ` <20101025111544.E773E63DD@mailscan3.ncs.mcgill.ca>
2010-10-25 14:26   ` property_vs_structure Marta Bunge
     [not found] ` <20101025012021.684BB8F88@mailscan2.ncs.mcgill.ca>
2010-10-25 19:30   ` property_vs_structure Marta Bunge

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