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From: Colin McLarty <colin.mclarty@case.edu>
To: Michael Shulman <shulman@math.uchicago.edu>,
	       categories <categories@mta.ca>
Subject: Re: Re: The omega-functor omega-category
Date: Sun, 3 Oct 2010 09:32:23 -0400	[thread overview]
Message-ID: <E1P2jnM-0001cq-H0@mlist.mta.ca> (raw)
In-Reply-To: <E1P2OMq-0002pn-Hd@mlist.mta.ca>

I like this discussion by Mike Shulman.  And a propos of the related
discussion of terminology I note the terms here describe mathematical
features (very well, I think) rather than focusing on whether one
*likes* the features.

2010/10/2 Michael Shulman <shulman@math.uchicago.edu>:

> I personally prefer to say that "unique choice structure" is something
> "in between" property and structure.  Kelly and Lack dubbed it
> "Property-like structure" in their paper with that title.  The
> difference is exactly as you say: property-like structure is unique
> (up to unique isomorphism) when it exists, but is not necessarily
> "preserved" by all morphisms.  In terms of forgetful functors,
> property-like structure corresponds to a functor which is
> *pseudomonic*, i.e. faithful, and full-on-isomorphisms.  Another nice
> example is that being a monoid is a "property" of a semigroup, i.e. a
> semigroup can have at most one identity element, but a semigroup
> homomorphism between monoids need not be a monoid homomorphism.

best, Colin


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  reply	other threads:[~2010-10-03 13:32 UTC|newest]

Thread overview: 33+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2010-09-23 10:07 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 [this message]
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   ` property_vs_structure Marta Bunge
     [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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