That proposal seems very odd to me. When we talk about categories, we almost always refer to them using their set of objects. For example, the category of groups (and group homomorphisms), or the functor category D^C (using the same exponential notation used for the underlying set of objects; the homs are natural transformations which have no such nice notation).
If we wanted to equip our algebraic objects with a category structure (for instance, the reals as a poset category), the objects would be the carrier and the homs would be something new. So everything seems to point to Obj = Base and Hom being a new slot. On Wed, Jan 29, 2020 at 8:32 AM Benoit <[email protected]> wrote: > Here is a question prompted by my remark in > https://groups.google.com/d/msg/metamath/Nvh_ue-PSBM/Nj-XpBvBAAAJ > "there is some gymnastic to do to put things in the right "slot", which > looks painful..." > > I see in ~df-cat that if c is a category, then ( Base " c ) is actually > the set of objects of c while the set of morphisms is denoted ( Hom " c ). > It looks a bit strange, and it would be more natural in my opinion to take > the set of morphisms as the base set, while having a slot ( Obj " c ) for > the set of objects of c. Is there a particular reason for choosing the > current convention ? Would it be possible to change it to the proposed > one, or would it be too much work ? > > Benoît > > -- > You received this message because you are subscribed to the Google Groups > "Metamath" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/metamath/12352990-c8ab-4df9-b031-d30c586b7ef8%40googlegroups.com > <https://groups.google.com/d/msgid/metamath/12352990-c8ab-4df9-b031-d30c586b7ef8%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- You received this message because you are subscribed to the Google Groups "Metamath" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/metamath/CAFXXJSuxF6UzA%2BRi6Cgx-SgZJmiBnWVk%2BhyoX%3DNf-Zo2_xggLA%40mail.gmail.com.
