In 1984, J. Rosický gave an abstract presentation of the structure associated to tangent
bundle functors in differential and algebraic geometry. By slightly generalizing this notion …

We establish close and previously unknown relations between quantales and groupoids. In
particular, to each étale groupoid, either localic or topological, there is associated a unital …

The reverse derivative is a fundamental operation in machine learning and automatic
differentiation. This paper gives a direct axiomatization of a category with a reverse …

We introduce monoidal streams: a generalization of causal stream functions to monoidal
categories. In the same way that streams provide semantics to dataflow programming with …

We introduce the normal produoidal category of monoidal contexts over an arbitrary
monoidal category. In the same sense that a monoidal morphism represents a process, a …

We introduce partial Markov categories. In the same way that Markov categories encode
stochastic processes, partial Markov categories encode stochastic processes with …

Reversible computation allows computation to proceed not only in the standard, forward
direction, but also backward, recovering past states. While reversible computation has …

Left restriction semigroups are a class of semigroups which generalise inverse semigroups
and which emerge very naturally from the study of partial transformations of a set.  …

A foundational theory of compositional categorical rewriting theory is presented, based on a
collection of fibration-like properties that collectively induce and intrinsically structure the …

Sesqui-pushout (SqPO) rewriting along non-linear rules and for monic matches is well-
known to permit the modeling of fusing and cloning of vertices and edges, yet to date, no …