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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeNov 9th 2010
• (edited Nov 9th 2010)

I created Lawvere distribution. I decided to formulate it directly in the $(\infty,1)$-topos setup, because

1. there the analogy with distributions makes (even) better sense, as we can invoke $\infty$-groupoid cardinality to think of (tame) $(\infty,1)$-sheaves as $\mathbb{R}$-valued functions;

2. it reproduces then a special case of the discussion at Pr(∞,1)Cat and harmonizes with the interpretation in terms of $\infty$-vector spaces as described there.

• CommentRowNumber2.
• CommentAuthorDmitri Pavlov
• CommentTimeApr 14th 2020
• (edited Apr 15th 2020)

What exactly is the difference between a Lawvere distribution and a cosheaf (valued in a topos)? We have two different entries for them, but the definitions appear to be identical.

• CommentRowNumber3.
• CommentAuthorDmitri Pavlov
• CommentTimeApr 15th 2020

Both articles were (mostly) written around November 2010 by Urs Schreiber. So I guess the above question is mostly addressed to Urs.

Would it be appropriate to merge the two articles?

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeApr 15th 2020
• (edited Apr 15th 2020)

It’s always about the most useful way to retrieve information. If you think people looking for Lawvere distributions would benefit most from discovering the concept inside an entry on cosheaves, and vice versa, then best to merge the entries. If instead it helps to adopt a certain focus (as in concepts with an attitude) then best to keep them separate.

Also it’s about how much energy you are going to invest. If you have lots of energy to do a major edit on the topic, then major re-arrangements could be useful. In the extreme case that you have the energy to do full justice to the topics, it could well be indicated to erase both entries and start over from scratch. If however you don’t plan to do any substantial edits to either entry, then a mere shuffling around of the existing material may be unlikely to improve the situation for the reader.

So it depends. :-)

• CommentRowNumber5.
• CommentAuthorDmitri Pavlov
• CommentTimeApr 15th 2020

Added details to the definition. Made connection to cosheaves explicit. Corrected “finite colimits” to “small colimits” in one place. Added an example.

• CommentRowNumber6.
• CommentAuthorDmitri Pavlov
• CommentTimeApr 15th 2020

For now, I limited myself to making the connection to cosheaves explicit.