Re: property_vs_structure

[Marta Bunge <marta.bunge@mcgill.ca>]

Dear George,
Thank you for your comments and questions.  I will have to look closely into the conditions of coverings in your sense to make sure that the off-my-hat assertion that unramified maps are an example is indeed correct. Also, your remark about the path-lifting property being "categorically forced" upon you in your work with Aurelio is particularly interesting to me as you suggested. I will most certainly look into those two points. 
I am also familiar with the T-categories and lax algebras, so that the work of Clementino, Hoffman and yourself should be easy for me to understand.  I point out (in case you do not know this) that my paper "Coherent extensions and relational algebras", Trans. AMS 197 (1974) 355-390 introduces lax adjointness,  examines examples including the T-categories of Burroni, and gives a new analysis of the example of topological spaces in this new light.  I mentioned this paper to Maria Manuel Clementino the first time I heard her talk about this subject, as it was obviously relevant. 
However, in view of my imminent trip to Buenos Aires, where I will spend most of November, I doubt that I will find the time this week to look into all of that before I return. 
With best regards,Marta

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Marta Bunge
Professor Emerita
Dept of Mathematics and Statistics 
McGill UniversityBurnside Hall, Office 1005
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Montreal, QC, Canada H3A 2K6
Office: (514) 398-3810/3800  
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marta.bunge@mcgill.ca 
http://www.math.mcgill.ca/~bunge/
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