A perfect and faithful record

A Full and Faithful Nerve For

The notion of geometric nerve of a 2-category (Street, [18]) provides a full and faithful functor if regarded as defined on the category of 2-categories and lax 2-functors. Furthermore, lax 2-natural transformations between lax 2-functors give rise to homotopies between the corresponding sim-plicial maps. These facts allow us to prove a representation theorem of the general non abelian cohomolo...

Old faithful.

On generalizations of semiperfect and perfect rings

‎We call a ring $R$ right generalized semiperfect if every simple right $R$-module is an epimorphic image of a flat right $R$-module with small kernel‎, ‎that is‎, ‎every simple right $R$-module has a flat $B$-cover‎. ‎We give some properties of such rings along with examples‎. ‎We introduce flat strong covers as flat covers which are also flat $B$-covers and give characterizations of $A$-perfe...

Faithful tropicalisation and torus actions

For any affine variety equipped with coordinates, there is a surjective, continuous map from its Berkovich space to its tropicalisation. Exploiting torus actions, we develop techniques for finding an explicit, continuous section of this map. In particular, we prove that such a section exists for linear spaces, Grassmannians of planes (reproving a result due to Cueto, Häbich, and Werner), matrix...

Faithful Squashed Entanglement

Squashed entanglement is a measure for the entanglement of bipartite quantum states. In this paper we present a lower bound for squashed entanglement in terms of a distance to the set of separable states. This implies that squashed entanglement is faithful, that is, it is strictly positive if and only if the state is entangled. We derive the lower bound on squashed entanglement from a lower bou...