4 papers
Quotients-comprehensions duality in relational doctrines
Francesco Dagnino, Fabio Pasquali
We establish a duality between quotients and comprehensions in relational doctrines, a class of indexed posets modelling (a minimal fragment of) the calculus of relations. We show…
Projective covers, doctrines of algebras and the relational quotient completion
Francesco Dagnino, Fabio Pasquali
The extensional quotient completion of relational doctrines provides a common generalization of both the exact completion of categories with weak finite limits and the elementary q…
The Relational Quotient Completion
Francesco Dagnino, Fabio Pasquali
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 h…
Cauchy-completions and the rule of unique choice in relational doctrines
Francesco Dagnino, Fabio Pasquali
Lawvere's generalised the notion of complete metric space to the field of enriched categories: an enriched category is said to be Cauchy-complete if every left adjoint bimodule int…