Timeline for Is there a version of the "infinitary" disjunctive normal form theorem for topoi and slice categories?
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| Nov 21, 2018 at 10:07 | comment | added | Simon Henry | No problem, So I looked for the precise reference for this lemma. But I couldn't fint in MacLane et Moerdijk Sheaves in Geometry and logic, so I'm not so sure it is there. It appears as Theorem D4.5.15 in PT.Johnstone Sketches of an elephant. | |
| Nov 21, 2018 at 7:12 | comment | added | goblin GONE | Yep, sorry. Slip of the brain. | |
| Nov 21, 2018 at 5:53 | comment | added | Simon Henry | Topos here meant grothendieck topos. | |
| Nov 21, 2018 at 2:38 | comment | added | goblin GONE | I don't see how that lemma could be true. For example, consider $\kappa$ inaccessible, and let $\mathcal{T}$ denote the topos of all $\kappa$-small sets. Then $\mathcal{T}$ is a topos in which every epimorphism splits. But since $\mathcal{T}$ doesn't have all small colimits, it's not a topos of sheaves. | |
| Nov 19, 2018 at 23:28 | history | edited | Simon Henry | CC BY-SA 4.0 |
added 771 characters in body
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| Nov 19, 2018 at 23:08 | history | answered | Simon Henry | CC BY-SA 4.0 |