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• CommentRowNumber1.
• CommentAuthorzskoda
• CommentTimeApr 7th 2010

algebrad and additions at Nikolai Durov. The movie starts slow and boring but gets very interesting after a while when the topic develops.

• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTimeApr 7th 2010

I added the abstract and its translation. Unfortunately, the time limitation made him cut from the most interesting part.

• CommentRowNumber3.
• CommentAuthorTodd_Trimble
• CommentTimeApr 7th 2010

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeApr 7th 2010

I guess that's what it must mean, yes.

• CommentRowNumber5.
• CommentAuthorzskoda
• CommentTimeApr 7th 2010

Look at the video yourself, I may have misunderstood the point.

• CommentRowNumber6.
• CommentAuthorzskoda
• CommentTimeApr 8th 2010

Mike posted a very useful comment. I hope people will gradually extract more definitions from the video.

• CommentRowNumber7.
• CommentAuthorzskoda
• CommentTimeApr 11th 2010

I corrected slightly the entry.

• CommentRowNumber8.
• CommentAuthorzskoda
• CommentTimeApr 11th 2010

More corrections.

• CommentRowNumber9.
• CommentAuthorzskoda
• CommentTimeJan 7th 2011

I read more of the manuscript of Durov in Russian recently. I have an impression (I am in a hurry right now, but hope to be able to explain that soon) that the fact that the algebrads, i.e. monads in the 2-category of vectoids generalize symmetric operads, non-sigma operads and alike is sort of a manifestation of an idea which is very close in spirit to John Baez’s microcosmos-macrocosmos principle. Namely, one uses the cocontinuity of the functor and aprpopriate completeness axiom to get that classification of an object with some kind of structure is reflected in the structure of finite approximations which determine the algebrad. This way one gets series of operations, satisfying some relations, depending which kind of algebaric structures the vectoid classifies. To say it differently, the main examples come from classifying vectoids, they typically classify objects with certain structure. Then the endocell respects this and reads the finite-level structure from there. This gives a combinatorics similar to the combinatorics of operads (category of species for example is an intermediate step in the case of usual operads which come from a classifier for objects).

• CommentRowNumber10.
• CommentAuthorMike Shulman
• CommentTimeJan 13th 2011

Interesting. What is gained by working with vectoids rather than, say, locally presentable categories? Are there important vectoids that are not locally presentable?

• CommentRowNumber11.
• CommentAuthorzskoda
• CommentTimeJan 14th 2011

Right, this is a good question and I was just trying last about a week to equip myself with understanding of such variants. Hopefully I will be able to answer your question soon.

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