Changes between Initial Version and Version 1 of Ticket #31877, comment 14


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Timestamp:
05/31/21 08:00:28 (8 months ago)
Author:
gh-mjungmath
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  • Ticket #31877, comment 14

    initial v1  
    99> @gh-mjungmath I don't understand what you mean by forgetful functor. These are parents, and have nothing to do with functors. For example, there is a forgetful functor from `Rings -> Sets`, and applying that functor to `ZZ` still obtains `ZZ`. It still has all of the behavior of an object in `Sets`, but there is no reason to actually forget about the ring structure.
    1010
     11> IMO, it is better to pass that category information to the homset construction (which you can do) if you want to consider morphisms in a weaker category. This way you have less proliferation of "equal" parents and dealing with elements that maybe shouldn't have the additional structure. In this example, should you be able to add two integers that are in the `ZZ` as a `Sets` object? Plus, the category you want for the morphisms is a property of the morphism, not the parent.
     12
     13
    1114Then I don't understand why we even have a forgetful functor if it technically just represents the identity functor...