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Jul 29, 2021 at 0:04 vote accept Emilio Minichiello
Jul 29, 2021 at 0:04 comment added Emilio Minichiello Ah, perfect! Thank you so much!
Jul 28, 2021 at 17:31 comment added Simon Henry I've added a short discusion on the fact that this map of span is cartesian, it actually only use universaility of coproduct. Re. your first comment I just mean that as both R and $X \times_E X$ are subobject of $X \times X$ and the map between them is an inclusion of subobjects, and hence a monomorphism (more formally, I'm using that if $f\circ g$ is a monomorphisms, then $g$ also is).
Jul 28, 2021 at 17:14 history edited Simon Henry CC BY-SA 4.0
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Jul 28, 2021 at 15:44 comment added Emilio Minichiello Could you also say a bit more on how disjoint and universal coproducts implies the map of spans in the lemma is cartesian?
Jul 28, 2021 at 14:40 comment added Emilio Minichiello This is a wonderful answer, thank you! Before I accept it, I have a question. Why at the end were you able to conclude that the morphism was a mono?
Jul 27, 2021 at 19:53 history edited D.-C. Cisinski CC BY-SA 4.0
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Jul 27, 2021 at 19:44 history edited Simon Henry CC BY-SA 4.0
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Jul 27, 2021 at 19:31 history answered Simon Henry CC BY-SA 4.0