REMARK ON SUBOBJECTS IN A TOPOS

On subobjects in categories

A Logic on Subobjects and Recognizability

We introduce a simple logic that allows to quantify over the subobjects of a categorical object. We subsequently show that, for the category of graphs, this logic is equally expressive as second-order monadic graph logic (msogl). Furthermore we show that for the more general setting of hereditary pushout categories, a class of categories closely related to adhesive categories, we can recover Co...

A remark on Remainders of homogeneous spaces in some compactifications

‎We prove that a remainder $Y$ of a non-locally compact‎ ‎rectifiable space $X$ is locally a $p$-space if and only if‎ ‎either $X$ is a Lindel"{o}f $p$-space or $X$ is $sigma$-compact‎, ‎which improves two results by Arhangel'skii‎. ‎We also show that if a non-locally compact‎ ‎rectifiable space $X$ that is locally paracompact has a remainder $Y$ which has locally a $G_{delta}$-diagonal‎, ‎then...

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

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...