Timeline for morita equivalence for categories
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| S Mar 29, 2021 at 1:00 | history | suggested | misseuler | CC BY-SA 4.0 |
moved dead link to current
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| Mar 28, 2021 at 23:55 | review | Suggested edits | |||
| S Mar 29, 2021 at 1:00 | |||||
| Jan 16, 2012 at 4:26 | comment | added | Benjamin Steinberg | A notable exception being 1-object categories that are not groups :) | |
| Jan 15, 2012 at 23:03 | comment | added | Tom Leinster | In practice, most commonly-encountered categories are already Cauchy complete. For example, any category with finite limits or with finite colimits is Cauchy complete. For such categories, Cauchy-completion does nothing, so the categories of presheaves on them are equivalent if and only if they themselves are equivalent. | |
| Jan 15, 2012 at 23:03 | comment | added | Tom Leinster | In a sense there's nothing to add to Finn's answer: it's a necessary and sufficient condition. But I'll add something anyway, in case the nLab page seems too daunting. Given maps p: A -> B and i: B -> A in a category such that pi = 1, the map ip is idempotent. An idempotent is said to be "split" if it is of this form. A category is said to be "Cauchy complete" if all idempotents in it are split. You can always Cauchy-complete a category, by throwing in a splitting for each idempotent. | |
| Jan 15, 2012 at 21:32 | history | answered | Finn Lawler | CC BY-SA 3.0 |