Timeline for Fully faithful functor from schemes to spaces
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Apr 5, 2019 at 18:02 | history | bounty ended | CommunityBot | ||
| S Apr 5, 2019 at 18:02 | history | notice removed | CommunityBot | ||
| S Mar 28, 2019 at 16:50 | history | bounty started | CommunityBot | ||
| S Mar 28, 2019 at 16:50 | history | notice added | user74900 | Draw attention | |
| Mar 26, 2019 at 20:10 | comment | added | user74900 | @ReidBarton let $a(X)$ be the cardinality of the underlying topological space of a scheme $X$ and let $b(X)$ be the cardinality of the disjoint union of the stalks of the structure sheaf of $X$ at all points. The construction in the linked answer satisfies $|F(X)|=a(X)+2^{b(X)}$. Is it possible to find a faithful functor $G$ such that say $|G(X)|\leq a(X)+b(X)$? | |
| Mar 26, 2019 at 17:07 | comment | added | Tim Campion | There's some related work by Trnkova, Pultr, and others -- keyword "universal categories". According to the introduction of Universal concrete categories and functors, every concrete category fully embeds into the category of topological spaces and open maps; this is apparently shown in Combinatorial, algebraic and topological representations of groups, semigroups and categories. | |
| Mar 26, 2019 at 16:59 | comment | added | Reid Barton | The category of schemes has a faithful functor to the category of sets (see mathoverflow.net/a/160768) and therefore also a faithful functor to topological spaces. | |
| Mar 26, 2019 at 11:53 | comment | added | Praphulla Koushik | If there exists/does not exists such a functor, what is the next thing you are interested to in? | |
| Mar 26, 2019 at 11:35 | review | First posts | |||
| Mar 26, 2019 at 12:08 | |||||
| Mar 26, 2019 at 11:34 | history | asked | user137517 | CC BY-SA 4.0 |