Timeline for Are regular epi of locale stably epic?
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| May 5, 2015 at 14:30 | comment | added | Simon Henry | @DominicvanderZypen : Here it is. | |
| May 5, 2015 at 14:29 | history | edited | Simon Henry | CC BY-SA 3.0 |
added 2293 characters in body
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| Apr 29, 2015 at 9:00 | comment | added | Dominic van der Zypen | Cool - I'm looking forward to the new formulatin! | |
| Apr 29, 2015 at 8:37 | comment | added | Simon Henry | Well, I already do it before I asked the question, and I didn't find the answer myself. But you are right: even if I prefer the "geometric" formulation, it cannot arm to give a second a formulation with the detail of the construction. I will do it as soon as I have a bit more time. | |
| Apr 29, 2015 at 8:18 | comment | added | Dominic van der Zypen | I believe the question would benefit from a re-formulation in terms of frames and the explicit construction of the pushout. Maybe doing this exact work, you even find the answer yourself! | |
| Apr 19, 2015 at 11:56 | comment | added | Simon Henry | $S'$ is any frame. and the pushout depends on $S'$ | |
| Apr 17, 2015 at 14:15 | comment | added | Dominic van der Zypen | What is $S'$? Can you write down $P$ in terms of $S$ and $L$, and also the pushout map? Thanks! | |
| Apr 17, 2015 at 11:35 | comment | added | Simon Henry | no you construct the pushout of $\iota$ along a map from $S$ to $S'$. And it will be the map from $L$ to the tensor product $L \otimes_{S} S'$ (the tensor product is the tensor product of sup-lattice). also note that not any frame monomorphism is a regular monomorphism. | |
| Apr 17, 2015 at 9:27 | comment | added | Dominic van der Zypen | Sorry for bothering you with stupid questions. Let $L$ be a frame, $S\subseteq L$ be a subframe and $\iota:S\to L$ be the inclusion map. So $\iota$ is regular. Q1: How do we construct the pushout object $P$ along $\iota$, or in other words, what is $P$? Q2: The "pushout morphism", what does it look like, does it go from $P$ or into $P$? Many thanks. | |
| Apr 14, 2015 at 9:21 | comment | added | Simon Henry | Yes. and locale monomorphism are just injective map, regular mono are equalizer of a pair of map (I don't know any nice characterisation), and by pushout I mean pushout (I.e. tensor product) along any frame morphism $X \rightarrow X'$. | |
| Apr 14, 2015 at 9:04 | comment | added | Dominic van der Zypen | Excuse me for a basic question, but I prefer to think in the "original" directions of maps. So in terms of frames and the category $\textbf{Frm}$, your question would be: Given frames $X,Y$, and a regular frame monomorphism $\iota: X\to Y$, is the pushout of $\iota$ necessarily mono? | |
| Sep 10, 2014 at 8:13 | history | asked | Simon Henry | CC BY-SA 3.0 |