Remark on Lomonosov’s lemma

A Relative Yoneda Lemma (manuscript) a Remark of the Referee

We construct set-valued right Kan extensions via a relative Yoneda Lemma. As the referee pointed out, (2.1) 'can essentially be found in much greater generality' in Therefore, we withdraw this note as a preprint. Since (2.1, 3.1) might be of some use for the working mathematician, we leave it accessible as a manuscript. In using (2.1), the reader should refer to [Ke 82], in using (3.1), he shou...

Remark on Taylor's Formula

does not contain any point of Er other than p. Cp(r]) is defined as in (5). From this it can be shown that Er has finite (n —1)-dimensional measure. Let us not assume now that r is large. We then write E = UjLxE^ where the E's are closed and their diameter is less than €. Then, by what has been shown before, if e is small enough Ef* has finite (w —1)-dimensional measure. Clearly ErCUjLxE?^'. Bu...

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

Remark on Loop Spaces

This theorem may be proved as an application of Stasheff's theory of yl „-spaces, and has certainly been noted by Stasheff. A method of proof was outlined in [3] in order to prove Corollary 3.12 of that paper, but the proof was defective.2 We give here a proof whose structure is essentially dual to that of the structure of the proof of Theorem A in [l], but which is much simpler in detail. Just...

Remark on a Reply

1.1 In their original PNAS article Macy and Sato (2002) make it clear that their main point concerns social mobility (see, for instance, the abstract and the last section). Their central claim is the non-monotonic effect of mobility: with moderate mobility, they maintain, trust can be established; with too much mobility, trust and trustworthiness are undermined — and therefore their "warning fl...