Timeline for What do people mean by "subcategory"?
Current License: CC BY-SA 2.5
4 events
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| May 13, 2010 at 3:32 | comment | added | Peter LeFanu Lumsdaine | yes, you're right --- my suggested coding did unintentionally change the functor. but as you say, this can be fixed --- you have to hack a little harder (to get around the fact that the multiplication table wants to talk about itself, which in the standard ZFC implementation it can't "literally" do) but yep, it does still work. | |
| May 13, 2010 at 0:14 | comment | added | Ben Wieland | I was thinking of modifying the ambient category, replacing NonEmptySets with the category whose objects are groups, but whose morphisms are maps of sets, ignoring the groups structure. It should be possible to define groups as special sets, but if you change the cardinality, as you and Peter LeFanu Lumsdaine (in the comments at top) do, this changes the functor from groups to sets. But I think you can stuff the multiplication table into the identity element. You just have to change the name of the identity in the table. But, mainly, I was just thinking thinking that Grps -> Sets is faithful. | |
| May 12, 2010 at 23:41 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
added 1 characters in body
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| May 12, 2010 at 23:33 | history | answered | Pete L. Clark | CC BY-SA 2.5 |