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    • Created page, mainly to record/redirect the alternate name “elementary existential doctrine” and some references.

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • added under “Selected writings” the articles cited elsewhere on the nLab

      diff, v2, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • [deleted]

    • I fixed a link to a pdf file that was giving a general page, and not the file!

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

      Anonymous

      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.

    • Mention the Yoneda embedding/free cocompletion which was somehow not referenced before.

      diff, v13, current

    • In the definition, the article states "every object in C is a small object (which follows from 2 and 3)". The bracketed remark doesn't seem quite right to me, since neither 2 nor 3 talk about smallness of objects. Presumably this should better be phrased as in A.1.1 of HTT, "assuming 3, this is equivalent to the assertion that every object in S is small".

      Am I right? I don't (yet) feel confident enough with my category theory to change this single-handedly.

    • I added a little bit of material to ordered field, namely that a field is orderable iff it is a real field (i.e., −1-1 is not a sum of squares). More importantly, at real closed field, I have addressed an old query of Colin Tan:

      Colin: Is it true that real closure is an adjoint construction to the forgetful functor from real closed fields to orderable fields?

      by writing out a proof (under Properties) that indeed the forgetful functor from category of real closed fields and field homomorphisms to the category of real fields and field homomorphisms has a left adjoint (the real closure). Therefore I am removing this query from that page over to here.

    • I added to field a mention of some other constructive variants of the definition, with a couple more references.

    • concerning the discussion here: notice that an entry rig category had once been created, already.

    • Added a lemma about fully faithful functors.

      Sorry for the mess, there does not seem to be a way to preview edits.

      diff, v3, current

    • Domenico Fiorenza started a page for the thesis of his student, Alessandra Capotosti: From String structures to Spin structures on loop spaces.

      Am I right in thinking the main innovation is the passage from the map

      BSpin conn→B 2(BU(1) conn) \mathbf{B}Spin_{conn} \rightarrow {\mathbf{B}}^2({\mathbf{B}}U(1)_{conn})

      to

      BSpin→B 2(BU(1) conn)? \mathbf{B}Spin \rightarrow {\mathbf{B}}^2({\mathbf{B}}U(1)_{conn})?

      Is that likely to work more generally, e.g., can one do something similar with

      BString conn→B 7U(1) conn? \mathbf{B}String_{conn} \rightarrow {\mathbf{B}}^7 U(1)_{conn}?

    • added to supergravity Lie 6-algebra a brief discussion of how the equations of motion of 11-d supergravity encode precisely the “rheonomic” ∞\infty-connections with values in the supergravity Lie 6-algebra.

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

      v1, current

    • I worked on Nonabelian Algebraic Topology

      • made the entry “category: reference”. all about the book by Brown et al – if we feel we need a more generic entry with lower case title later, we can still split it off again

      • then I started adding a “Contents” section similar to what we have at Elephant and Higher Topos Theory etc., and started adding some of the content of relevance for the cosmic cube.

    • I have been editing the entry homotopy equivalence to include a brief discussion of strong homotopy equivalences and Vogt's lemma. In so doing, I have followed my nose and found various other entries to edit. For instance that for Hans Baues, that for cylinder functor, etc. I am thinking that the general area of Henry Whitehead's idea of algebraic homotopy, may be a useful intermediate one between the infinity category ideas (which could be seen as just a 'souped up' version of Kan complexes), (I am not saying they are just that a cynic might make them out to be!) and the algebraic topologists desire to perform calculations. Note the quotes at algebraic homotopy. Of course, they d not say what 'compute' means in this context. (Note we do not have an entry on Whitehead as yet.)

    • Fixed a broken link to Jardine’s lectures.

      This article references Jardine’s lectures for a cubical subdivision functor, but I could not find it in this source. Is cubical subdivision described elsewhere?

      diff, v4, current

    • For no particular reason, I have added another illustrating graphics to the entry, taken from Fig 1.3 in Apostol 1973.

      diff, v19, current

    • A comparatively long and technical section “From hom-functors to units and counits” (on adjoint functors) was sitting inside the Idea-section of adjunction. It seemed plainly misplaced there, and distracting attention from what should be the content of this entry, as opposed to the entry adjoint functor. So I have moved it now to where it seems to belong: inside the Examples-section.

      diff, v55, current

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