Delta lenses are functors equipped with a functorial choice of lifts, and specialise to split opfibrations when these lifts are opcartesian. In this talk, I will reflect on some of the many similarities between the rich theory of split opfibrations and the growing theory of delta lenses, and outline some yet unanswered questions. In particular, I will explore possible…

We study the concept of the l_p-Vietoris-Rips simplicial set and the l_p-Vietoris-Rips simplicial complex of a metric space, where 1≤p≤∞. For  p=∞  we obtain the classical theory of Vietoris-Rips complexes, and for p=1 we obtain the simplicial set, whose homology is the blurred magnitude homology. We prove several results that were known for the Vietoris-Rips complex in…