Re: Re: The omega-functor omega-category

[Colin McLarty <colin.mclarty@case.edu>]

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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