Timeline for Categories that admit all products but not all coproducts
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Mar 10 at 14:14 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| Mar 10 at 5:04 | comment | added | Corbin | Another important family not yet mentioned are Cartesian closed categories, particularly those which are freely generated by simply-typed lambda calculi (WP, nLab); coproducts are a separate ingredient not addressed by their syntax, but products are implied by the builtin curry (WP, nLab). (This would have been an answer, but it fits in a comment!) | |
| Mar 9 at 23:41 | comment | added | Tim Campion | @DenisT Thanks! Apparently this fact (injectives closed under coproducts iff Noetherian) is known as the Bass-Papp theorem. | |
| Mar 9 at 23:22 | history | edited | LSpice | CC BY-SA 4.0 |
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| Mar 9 at 18:14 | comment | added | Denis T | The term colloquially used for rings $R$, injective left modules over which are closed under coproducts (or, nontrivially equivalently, closed under coproducts indexed by a set of cardinality $|R|$), is left noetherian. | |
| Mar 9 at 17:47 | history | edited | Tim Campion | CC BY-SA 4.0 |
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| Mar 9 at 17:41 | history | edited | Tim Campion | CC BY-SA 4.0 |
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| Mar 9 at 17:36 | history | answered | Tim Campion | CC BY-SA 4.0 |