[FOM] two interpretations of identity morphisms in category theory

Paul Hollander paul at personalit.net
Wed May 3 15:00:45 EDT 2017

On 4/30/17 23:08, Patrik Eklund wrote:
> Traditionally we train students saying "these are the objects, and the 
> morhpisms are ...". However, if we look back e.g. at Ehresmann et co's 
> algebraic view on categories dating back to the 1950s, there are 
> notions of identities where seemingly morphisms precede objects. It 
> appears implicitly in Menger's paper's from that time, so even Newton 
> had some intuition of "identity" which is not overwritten today in any 
> way, I would say.

I had the somewhat unique experience of being born with Ectopia Lentis 
Syndrome, caused by Marfan Syndrome, a genetic disease of the connective 
tissue.  Consequently, my vision was worse than 20/200 with correction 
from birth through age 12 (the eighth grade) when I finally had access 
to qualified doctors and my vision was partially corrected so I could 
read a chalk board.

Consequently, I learned my basic arithmetic through basic algebra mostly 
by hearing and speech alone, never by reading a blackboard or equations 
at a distance.

To me, equations like '7+5=12' refer to activities, not objects.

But my peers tend to think of natural numbers as objects, not activities.

It was only as an undergraduate encountering Kant, Hegel and the 
Intuitionists for the first time, that I finally felt at home among 


Paul Hollander

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