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

The categorified theories known as “doctrines” specify a category equipped with extra
structure, analogous to how ordinary theories specify a set with extra structure. We introduce …

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 …

We extend the arithmetic product of species of structures and symmetric sequences studied
by Maia and Mendez and by Dwyer and Hess to coloured symmetric sequences and show …

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 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 …

In this work, we continue the investigation of certain enrichments of dual algebraic structures
in monoidal double categories, that was initiated in [Vas19]. First, we re-visit monads and …

In this article, we combine Sweedler's classic theory of measuring coalgebras--by which $ k
$-algebras are enriched in $ k $-coalgebras for $ k $ a field--with the theory of W-types--by …

We extend the arithmetic product of species of structures and symmetric sequences studied
by Maia and Méndez and by Dwyer and Hess to coloured symmetric sequences and show …

In this paper, we consider coalgebra measurings between Hopf algebroids and show that
they induce morphisms on cyclic homology and cyclic cohomology. We also consider …