Timeline for Naturally occurring examples of badly behaved categories
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 21, 2021 at 4:23 | comment | added | xuq01 | @MartinBrandenburg I guess it really depends on what counts as "well-behaved substitutes". For manifolds you can also pass to smooth spaces, although this is arguably a bigger stretch than passing to compactly-genenrated Hausdorff spaces. | |
| Apr 20, 2021 at 21:17 | comment | added | Martin Brandenburg | I wanted to say "countable coproducts" and "larger coproducts" - not general colimits of course. | |
| Apr 16, 2021 at 12:18 | comment | added | Martin Brandenburg | I would say that $\mathbf{Top}$ behaves much better than $\mathbf{Man}$. Notice that $\mathbf{Man}$ has finite products, but fiber products exist only in very good cases (cf. regular value theorem). Countable colimits exist, but larger colimits do not exist when you insist that manifolds should be secound-countable (so better choose paracompactness), and coequalizers usually don't exist either. For topological spaces, we just need to switch to one of the well-behaved substitutes (like compactly generated Hausdorff spaces) to get a bicomplete ccc. This is not possible for manifolds. | |
| S Apr 15, 2021 at 6:28 | history | answered | xuq01 | CC BY-SA 4.0 | |
| S Apr 15, 2021 at 6:28 | history | made wiki | Post Made Community Wiki by xuq01 |