We introduce the calculus of neo-Peircean relations, a string diagrammatic extension of the
calculus of binary relations that has the same expressivity as first order logic and comes with …

Taking a quotient roughly means changing the notion of equality on a given object, set or
type. In a quantitative setting, equality naturally generalises to a distance, measuring how …

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 …

Taking a quotient roughly means changing the notion of equality on a given object, set or
type. In a quantitative setting, equality naturally generalises to a distance, measuring how …

Fo-bicategories are a categorification of Peirce's calculus of relations. Notably, their laws
provide a proof system for first-order logic that is both purely equational and complete. This …

What is ergonomic syntax for relations? In this first paper in a series of two, to answer the
question we define regular calculi: a suitably structured functor from a category representing …

Lawvere's hyperdoctrines (or simply doctrines)[7, 8] provide a fairly simple and intuitive
categorical framework for studying severl kinds of logics. Indeed, a doctrine is just a functor …

Background Cartesian bicategories (of relations) were introduced in [2] by Carboni and
Walters as a categorical algebra of relations. These are poset-enriched categories such that …