In previous work, we develop a generalized Waldhausen $S_{\bullet}$-construction whose input is an augmented stable double Segal space and output unital 2-Segal space. Here, prove that this construction recovers the previously known $S_{\bullet}$-constructions for exact categories $(\infty,1)$-categories, as well relative functors.

This paper discusses a class of French à-infinitival constructions, where the missing direct object corresponds to an external argument, either being antecedent noun in attributive use, or else raised argument subject predication tough construction.  We investigate internal and properties these constructions show that (i) construction displays passive-like (ii) control raising verbs ma...

Origami is an ancient art that continues to yield both artistic and scientific insights this day. In 2012, Buhler, Butler, de Launey, Graham extended these ideas even further by developing a mathematical construction inspired origami -- one in which we iteratively construct points on the complex plane (the "paper") from set of starting (or "seed points") lines through those with prescribed angl...

In this work, we survey some research directions in which the ultraproduct construction and methods based on ultrafilters play significant roles. Rather different areas of mathematics have been considered: topics are reviewing here include aspects model theory first-order second-order existential logics, finite Ramsey general topology. Special emphasis has made for producing a uniform treatment...