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- Discussion Type
- discussion topicacyclic object
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 23rd 2010

a little acyclic object

- Discussion Type
- discussion topicOka
- Category Latest Changes
- Started by zskoda
- Comments 11
- Last comment by zskoda
- Last Active Nov 22nd 2010

New stubs Oka principle, Oka manifold (with redirect Oka map) and Franc Forstnerič. Jardine has shown that one can use the Toen-Vezzosi like engineering with his intermediate model structure on the category of simplicial presheaves on a simplicial version of the Stein site. The $(\infty,1)$-stacks/fibrants will be Oka maps; those cofibrants which are represented by complex manifolds are in fact Stein manifolds.

- Discussion Type
- discussion topicfuture cone
- Category Latest Changes
- Started by Tim_Porter
- Comments 2
- Last comment by Tim_Porter
- Last Active Nov 22nd 2010

created a stub future cone. This was in the context of directed homotopy theory, but clearly could be developed and linked to other topics.

- Discussion Type
- discussion topicChoice functions
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Nov 19th 2010

New: choice function

- Discussion Type
- discussion topicVopenka's principle
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Mike Shulman
- Last Active Nov 19th 2010

expanded Vopenka’s principle

- Discussion Type
- discussion topicmodel structure on monoids in a monoidal model category
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Nov 18th 2010

stub for model structure on monoids in a monoidal model category, for the moment only to host Schwede-Shipley’s lemma on homotopy pushouts along free monoid morphisms

- Discussion Type
- discussion topicmonoid axiom in a monoidal model category
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 18th 2010

- Discussion Type
- discussion topictensor power
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 18th 2010

tried to brush-up tensor power a little

- Discussion Type
- discussion topicmodel structure on algebras over a monad
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 18th 2010

- Discussion Type
- discussion topicmodel structure on algebras over an operad
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Nov 17th 2010

am working on model structure on algebras over an operad.

- Discussion Type
- discussion topicover-topos and base change
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active Nov 17th 2010

I expanded some entries related to the Café-discussion:

at over-(infinity,1)-topos I expanded the Idea-section, added a few remarks on proofs and polished a bit,

and added the equivalence $\infty Grpd/X \simeq PSh_{\infty}(X)$ to the Examples-section

at base change geometric morphism I restructured the entry a little and then included the proof of the existence of the base change geometric morphism

- Discussion Type
- discussion topiclimits in over-(oo,1)-categories
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 17th 2010

wrote out the proof of the expected statement at limits in over-(oo,1)-categories

- Discussion Type
- discussion topicadjunct
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 17th 2010

added to adjunct the description in terms of units and counits.

- Discussion Type
- discussion topic(oo,1)-algebraic theory
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active Nov 17th 2010

created (infinity,1)-algebraic theory.

I tried to adapt Rosicky’s and Lurie’s terminology such as to match that at algebraic theory, but Mike, Toby, Todd and whoever else feels expert should please check if I did it right.

- Discussion Type
- discussion topicFAC
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Nov 15th 2010

New reference entry FAC aka Faisceaux algébriques cohérents. And few improvements to coherent sheaf including historical note.

- Discussion Type
- discussion topicoo-sheaves over paracompact spaces
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 15th 2010

- Discussion Type
- discussion topicPr(oo,1)Cat
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 15th 2010

added some propositions to Pr(infinity,1)Cat that support the analogy to linear algebra, as described there and at integral transforms on sheaves

- Discussion Type
- discussion topicmodel structure on operator algebras
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by Tim_Porter
- Last Active Nov 15th 2010

- Discussion Type
- discussion topicNew: ordered field
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Nov 15th 2010

I satisfied a few requests for ordered field. Pretty basic.

- Discussion Type
- discussion topicblob homology
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Tim_Porter
- Last Active Nov 12th 2010

Kevin Walker was so kind to add a bit of material to blob homology. Notably he added a link to a set of notes now available that has more details.

I added formatting and some hyperlinks.

- Discussion Type
- discussion topicBoardman-Vogt resolution
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Nov 12th 2010

stub for Boardman-Vogt resolution

- Discussion Type
- discussion topicE-oo algebra
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 11th 2010

edited E-infinity algebra a little. Still all very stubby

- Discussion Type
- discussion topicloop spaces and H-spaces
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Nov 11th 2010

I added to loop space a reference to Jim’s classic article, which was only linked to from H-space and put pointers indicating that his delooping result in $Top$ is a special case of a general statement in any $\infty$-topos.

By the way: it seems we have slight collision of terminology convention here: at “loop space” it says that H-spaces are homotopy associative, but at “H-space” only a homotopy-unital binary composition is required, no associativity. I think this is the standard use. I’d think we need to modify the wording at loop space a little.

- Discussion Type
- discussion topicA-oo algebra
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active Nov 11th 2010

I reworked A-infinity algebra so as to apply to algebras over any $A_\infty$-operad in any ambient category. So I created subsections “In chain complexes”, “In topological spaces”.

I think if we speak generally of “algebra over an operad” then we should also speak generally of “$A_\infty$-algebra” even if the enriching category is not chain complexes. Otherwise it will become a mess. But I did link to A-infinity space.

- Discussion Type
- discussion topiccoloured operad
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Nov 10th 2010

added the definition of “coloured operad” to operad in the section “Rough definition”

(by the way, should we not rather call these “pedestrian definition” or so instead of “rough”? The latter seems to suggest that there is something not quite working yet with these definitions, while in fact they are perfectly fine, just not as high-brow as other definitions.)

- Discussion Type
- discussion topicmodel structure on modules over an algebra over an operad
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 10th 2010

created stub for model structure on modules over an algebra over an operad

- Discussion Type
- discussion topicmodule over an algebra over an operad
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 10th 2010

created stub for module over an algebra over an operad

- Discussion Type
- discussion topictransgression
- Category Latest Changes
- Started by Eric
- Comments 81
- Last comment by Urs
- Last Active Nov 10th 2010

I started an idea section at transgression, but it could probably use some going over by an expert. I hope I didn’t mess things up too badly. I was reading Urs’ note on “integration without integration” on the train ride home and fooled myself into thinking I understood something.

By the way, this reminded me of a discussion we had a while back

- Discussion Type
- discussion topicresolutions of operads
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 10th 2010

started a section on cofibrant resolutions at model structure on operads. But incomplete for the time being.

- Discussion Type
- discussion topicmodel structure on spectra
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 10th 2010

stub for model structure on spectra