It is proved that in any pointed category with pullbacks, coequalizers and regular epi-mono factorizations, the class of regular epimorphisms is stable under pullback along the so-called balanced effective descent morphisms. Here “balanced” can be omitted if the category is additive. A balanced effective descent morphism is defined as an effective descent morphism p : E → B such that any subobj...

For most of the time, biomedical researchers have been dealing with ordinal outcome variable in multilevel models where patients are nested in doctors. We can justifiably apply multilevel cumulative logit model, where the outcome variable represents the mild, severe, and extremely severe intensity of diseases like malaria and typhoid in the form of ordered categories. Based on our simulation co...

We show that the Witt class of a weakly group-theoretical non-degenerate braided fusion category belongs to the subgroup generated by classes of non-degenerate pointed braided fusion categories and Ising braided categories. This applies in particular to solvable nondegenerate braided fusion categories. We also give some sufficient conditions for a braided fusion category to be weakly group-theo...

We introduce a relative semi-abelian category as a pair (C,E), where C is a pointed category with finite limits, and E is a class of normal epimorphisms in C satisfying certain conditions, stronger than those defining a relative homological category [2]. In the absolute case, i.e. when E is the class of all regular epimorphisms in C, the pair (C,E) is relative semi-abelian if and only if C is s...

The topic I’d like to talk to you about today is, I think, one of the oldest and most basic in cognition: how we learn from examples. As most famously pointed out by Hume, when we make a finite number of observations of an enduring phenomenon, there is no strictly logical (i.e., deductive) basis for forming any firm generalizations about it. Instead we must “induce,” that is, make educated gues...

We describe a homotopy-theoretic approach to the theory of moduli realizations Blanc-Dwyer-Goerss, reproducing their obstructions realizing given Π-algebra as homotopy groups pointed space. Our techniques are based on ∞-category PΣ(Sph) product-preserving presheaves finite wedges positive-dimensional spheres, leading more conceptual and streamlined arguments.