Category theory is a branch of mathematics that provides a formal framework for
understanding the relationship between mathematical structures. To this end, a category not …

Via the adjunction-∗ 1⊣ V (1,-): Span (V)→ V-Mat and a cartesian monad T on an extensive
category V with finite limits, we construct an adjunction-∗ 1⊣ V (1,-): Cat (T, V)→(T¯, V)-Cat …

Products in double categories, as found in cartesian double categories, are an elegant
concept with numerous applications, yet also have a few puzzling aspects. In this paper, we …

Structured and decorated cospans are broadly applicable frameworks for building
bicategories or double categories of open systems. We streamline and generalize these …

We introduce contextads and the Ctx construction, unifying various structures and
constructions in category theory dealing with context and contextful arrows--comonads and …

Given a cartesian closed category $\mathcal {V} $, we introduce an internal category of
elements $\int_\mathcal {C} F $ associated to a $\mathcal {V} $-functor $ F\colon\mathcal …

Abridged abstract: In this article we develop formal category theory within augmented virtual
double categories. Notably we formalise the notions of Kan extension and Yoneda …

Many structures of interest in two-dimensional category theory have aspects that are
inherently strict. This strictness is not a limitation, but rather plays a fundamental role in the …

We define limits for diagrams valued in an $(\infty, n) $-category. As a model of $(\infty, n) $-
categories, we use complete Segal objects in $(\infty, n-1) $-categories. We show that this …

In probabilistic modelling, joint distributions are often of more interest than their marginals,
but the standard composition of stochastic channels is defined by marginalization. Recently …