Timeline for Tensored and cotensored simplicial comma category
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
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| Mar 8, 2022 at 16:12 | history | edited | Philippe Gaucher | CC BY-SA 4.0 |
added 37 characters in body
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| Mar 8, 2022 at 16:04 | comment | added | Tim Campion | My own preference -- define the simplicial enrichment on $C \downarrow Z$ by $Hom(X \xrightarrow f Z, Y \xrightarrow g Z) = Hom(X,Y) \times_{Hom(X,Z)} \{f\}$ and then derive the tensoring and cotensoring formulas via computations from this definition. Even better, the simplicial hom formula that I just wrote down can itself be derived as a computation if you define the simplicially-enriched category $C \downarrow Z$ by the appropriate 2-categorical universal property in the 2-category of simplicially-enriched categories (which is well-known to be 2-categorically complete and cocomplete). | |
| Mar 8, 2022 at 15:53 | history | asked | Philippe Gaucher | CC BY-SA 4.0 |