Timeline for In which categories is the union of subobjects given by the pushout over the intersection?
Current License: CC BY-SA 4.0
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| Jan 5, 2023 at 6:02 | history | edited | Tim Campion | CC BY-SA 4.0 |
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| Jan 5, 2023 at 3:56 | vote | accept | Tim Campion | ||
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| Jan 5, 2023 at 3:56 | history | edited | Tim Campion | CC BY-SA 4.0 |
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| Jan 2, 2023 at 18:22 | comment | added | Tim Campion | I think the proof of Thm 4.7 only uses that pushouts of monos are stable under pullback, not the full strength of adhesiveness. | |
| Jan 2, 2023 at 18:18 | comment | added | Tim Campion | @varkor Here is what seems to be another version of the same paper (BRICS RS-03-31). Here, Theorem 4.7 and Corollary 4.8 have proofs. Thm 4.7 says that every adhesive category has effective unions, while Cor 4.8 shows that if unions are effective and pushouts of monos are stable under pullback along monos, the subobject lattices are distributive. So it seems the issue which prevents an abelian category from being adhesive is that pushouts of monos are not stable under pullback along monos. | |
| Jan 2, 2023 at 4:12 | comment | added | varkor | It appears the proofs of those statements are omitted from the paper entirely... | |
| Jan 2, 2023 at 0:14 | history | edited | Tim Campion | CC BY-SA 4.0 |
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| Jan 2, 2023 at 0:07 | history | answered | Tim Campion | CC BY-SA 4.0 |