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    • 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 Grpd/XPSh (X)\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

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

    • 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.

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

    • added the equivalence

      Top/XSh (,1)(X) Top/X \simeq Sh_{(\infty,1)}(X)


    • 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.

    • 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 TopTop 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.

    • I reworked A-infinity algebra so as to apply to algebras over any A 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 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.

    • 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.)

    • 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

      Integrals: Loops space vs target space

    • added very briefly the monoidal model structure on GG-objects in a monoidal model category to monoidal model category (deserves expansion)