We propose a categorical framework for processes which interact bidirectionally with both
an environment and a'controller'. Examples include open learners, in which the controller is …

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

One could argue [Eve17, Chapter 2] that counting is one of the first instances of abstraction
in the history of the human species. At some point, not later than 10.000 years ago 1 …

The contributions of this paper are twofold. Within the framework of Grothendieck's
fibrational category theory, we present a web of fundamental 2-adjunctions surrounding 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 contribute to expand 2-dimensional elementary topos theory. We focus on the concept of
2-classifier, which is a 2-categorical generalization of the notion of subobject classifier. The …

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 …

The present paper aims at stressing the importance of the Hofmann–Streicher groupoid
model for Martin Löf Type Theory as a link with the first-order equality and its semantics via …

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 …

We study the 2-category of elements from an abstract point of view. We generalize to
dimension 2 the well-known result that the category of elements can be captured by a …