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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

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    • Created page with sections for idea, definition, basic examples, basic references.

      Needs results, more examples, more references.

      v1, current

    • One small question that has often occurred to me:

      • in the three usual axioms specifying how the unit interacts with parenthesizing in a monoidal bicategory, is there any known reason for drawing one of the three diagrams as a square (as opposed to a triangle, like the other two) even though one of the 1-cells is the identity id\otimesid, except for the (certainly important) aesthetical/visual/psychological reason that otherwise (if using the conventional notation) the tip of the arrow giving the 2-cell would point from a 1-cell to a 0-cell?

      (Technical note: I chose the “Latest Changes” category, even though no change to monoidal bicategory was made yet, because monoidal bicategory appears to not have had a thread of its own yet, and it is not inconceivable that this page will evolve in the future and need a thread)

    • Page created, but author did not leave any comments.

      v1, current

    • added a bunch of references under Selected writings

      diff, v2, current

    • added to Yang-Mills instanton a discussion of instantons as tunnelings between Chern-Simons vacua.

    • Page created, but author did not leave any comments.

      v1, current

    • edited resource with corrected link.

      Anonymous

      diff, v8, current

    • Page created, but author did not leave any comments.

      v1, current

    • created a minimum at function monad (aka “reader monad”, “environment monad”)

    • This is my first (substantial) contribution to the nLab, so forgive my likely ineptitude. This wants to be a initial stub, everything is basically scraped from the reference and this post: https://golem.ph.utexas.edu/category/2019/07/structured_cospans.html Clearly a lot of material can be added, included a better definition and clearer examples. It’s also quite necessary to make a page for decorated cospans. I might start it myself later this month.

      mattecapu

      v1, current

    • created page, link to personal website, and a related pages section.

      v1, current

    • started a Properties-section at Lawvere theory with some basic propositions.

      Would be thankful if some experts looked over this.

      Also added the example of the theory of sets. (A longer list of examples would be good!) And added the canonical reference.

    • I fixed a trivial typo in adjoint functor theorem but left wondering about this:

      … the limit

      Lc:=lim cRdd L c := \lim_{c\to R d} d

      over the comma category c/Rc/R (whose objects are pairs (d,f:cRd)(d,f:c\to R d) and whose morphisms are arrows ddd\to d' in DD making the obvious triangle commute in CC) of the projection functor

      Lc=lim (c/RD). L c = \lim_{\leftarrow} (c/R \to D ) \,.

      I don’t really understand this (and while I could figure it out, it’s probably not good to make readers do so). At first it sounds like someone is saying “the limit LcL c over the comma category of the projection functor LcL c”, which would be circular. But it must be that both formulas are intended as synonymous definitions of LcL c. At that point one is left wondering why one has a backwards arrow under it and the other does not. I guess old-fashioned people prefer writing limits with backwards arrows under them, so someone is trying to cater to all tastes? I think it’s better in this website to use limlim and colimcolim for limit and colimit.

      I could probably guess how to fix this, but I won’t since I might screw something up.

    • There has been a pretty massive expansion at proof net. All who are interested in this are invited to have a look (but the nLab is super-slow in loading now from where I write).

      Noam Z., if you are reading this: I had looked at the notes you kindly mentioned to me recently. Could you comment on what the connection might be with the sequentialization result (see the remark 2 under theorem 1 in proof net)? The outline of proof reminded me of your description of inversion and focusing, but I confess I had a little trouble following everything (my fault, not yours).

    • stub, just to satisfy links for the moment

      v1, current

    • Page created, but author did not leave any comments.

      v1, current