Timeline for What are "nearly initial" objects really called?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Nov 1, 2021 at 8:06 | answer | added | Ivan Di Liberti | timeline score: 2 | |
| Dec 24, 2020 at 13:03 | answer | added | varkor | timeline score: 7 | |
| Dec 7, 2016 at 1:11 | history | edited | goblin GONE | CC BY-SA 3.0 |
added 13 characters in body
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| Dec 7, 2016 at 1:08 | vote | accept | goblin GONE | ||
| Dec 5, 2016 at 6:09 | answer | added | Tim Campion | timeline score: 4 | |
| Dec 5, 2016 at 5:56 | comment | added | მამუკა ჯიბლაძე | Yes weak initiality forces out the empty one. And even after that I was wrong - one needs connected $G$-sets (in other words, the transitive (single-orbit) ones) and coverings for my claims to hold | |
| Dec 5, 2016 at 5:53 | comment | added | goblin GONE | @მამუკაჯიბლაძე, I think you mean $G$ in the category of inhabited $G$-sets? And, is that really true? | |
| Dec 5, 2016 at 5:30 | comment | added | მამუკა ჯიბლაძე | Another example is the universal covering of a space, in the category of coverings. Accordingly, $G$ in the category of $G$-sets is such. | |
| Dec 5, 2016 at 1:32 | comment | added | Tim Campion | Also, the dual concept is also important. For example, saturated models and Fraisse limits have this "nearly terminal" property, at least with respect to other objects which are "small". To tie into Todd's remark, such objects can be constructed as injective hulls / Fraisse-type constructions, using back-and-forth arguments. I wrote a note about this here once. | |
| Dec 5, 2016 at 1:22 | comment | added | Tim Campion | I don't have a better name, but I do have a fun fact to share (a straightforward application of Quillen's Theorem A): If $\mathbf{C}$ has a nearly initial object $X$ and all morphisms out of $X$ are monomorphisms, then the classifying space of $\mathbf{C}$ is a $K(G,1)$ where $G = \mathbf{Aut}(X)$. | |
| Dec 5, 2016 at 0:56 | answer | added | Alexander Campbell | timeline score: 14 | |
| Dec 4, 2016 at 23:11 | comment | added | Todd Trimble | I've not seen this notion myself, but it reminds me of the notion of injective hull: ncatlab.org/nlab/show/injective+hull Algebraic closures are an example. | |
| Dec 4, 2016 at 14:14 | history | asked | goblin GONE | CC BY-SA 3.0 |