We lift the standard equivalence between fibrations and indexed categories to an
equivalence between monoidal fibrations and monoidal indexed categories, namely weak …

We develop a theory which unifies the universal (co) acting bi/Hopf algebras as studied by
Sweedler, Manin and Tambara with the recently introduced [AL Agore, AS Gordienko and J …

We introduce and study functor-functor and monad-comonad interaction laws as
mathematical objects to describe interaction of effectful computations with behaviors of effect …

We combine the theory of inductive data types with the theory of universal measurings. By
doing so, we find that many categories of algebras of endofunctors are actually enriched in …

The universal (co) acting bi/Hopf algebras introduced by Yu.\, I.~ Manin, M.~ Sweedler and
D.~ Tambara, the universal Hopf algebra of a given (co) module structure, as well as the …

As left adjoint to the dual algebra functor, Sweedler's finite dual construction is an important
tool in the theory of Hopf algebras over a field. We show in this note that the left adjoint to the …

In this work, we explore a double categorical framework for categories of enriched graphs,
categories and the newly introduced notion of cocategories. A fundamental goal is to …

We introduce the notion of an enriched fibration, ie a fibration whose total category and base
category are enriched in those of a monoidal fibration in an appropriate way. Furthermore …

We show that the universal measuring coalgebras between Frobenius algebras turn the
category of Frobenius algebras into a Hopf category (in the sense of Batista-Caenepeel …

We prove that given C a presentably symmetric monoidal∞-category, and any essentially
small∞-operad O, the∞-category of O-algebras in C is enriched, tensored and cotensored …