Timeline for Original reference for categories of presheaves as free cocompletions of small categories
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 12, 2021 at 15:27 | comment | added | Jochen Wengenroth | @MartinBrandenburg In the Lecture Notes, Lambek writes that this terminology was suggested by Amitsur, but he does not give a reference. | |
| Oct 12, 2021 at 13:13 | comment | added | Jochen Wengenroth | I like the terminology limit=infimum and colimit=supremum very much. For many diagrams limits or colimits are very poor approximations and only give very little information. This is very similar to infima and suprema in partially ordered sets. | |
| Jul 2, 2021 at 22:09 | comment | added | Tom Leinster | @MartinBrandenburg OK, never mind then. I unthinkingly assumed that the word "completion" in Lambek's title referred to a universal property, but that's a 2021 view of 1966. E.g. Isbell's 1966 paper "Structure of categories" contains this sentence (first paragraph): "By a completion of [a category] $A$ is meant a complete caegory in which $A$ is fully embedded so that no complete full proper subcategory contains it". | |
| Jul 2, 2021 at 21:07 | comment | added | Martin Brandenburg | Lambek doesn't mention or prove the universal property in that book. Also because he was mainly interested in cocompletions which preserve existing colimits. | |
| Jul 2, 2021 at 21:05 | comment | added | Martin Brandenburg | (offtopic) Did any other author except for Lambek use the terms "supremum" and "infimum" for "colimit" and "limit"? | |
| Jul 2, 2021 at 16:13 | comment | added | varkor | Thanks, this is a good suggestion. I took a look through and couldn't find a reference for this result, but it's a useful upper bound on when the result was known. | |
| Jul 2, 2021 at 16:01 | history | answered | Tom Leinster | CC BY-SA 4.0 |