Foreword 1. Abstract sets and mappings 2. Sums, monomorphisms and parts 3. Finite inverse limits 4. Colimits, epimorphisms and the axiom of choice 5. Mapping sets and exponentials 6. Summary of the… Expand

We show that the generic symmetric monoidal category with a commu- tative separable algebra which has a Σ-family of actions is the category of cospans of finite Σ-labelled graphs restricted to finite… Expand

This papershows that, given a factor ization system, E/M on a closed symmetric monoidal category, the full subcategory of separated extensional objects of the Chu category is also ∗-autonomous… Expand

The known characterization of nuclear sup lattices in set as completely distributive lattices is extended to yet another characterization of (CCD) lattice in a topos and aknown characterization of projective frames is recovered.Expand

Abstract We pursue distributive laws between monads, particularly in the context of KZ-doctrines, and show that a very basic distributive law has (constructively) completely distributive lattices for… Expand

This paper presents a new treatment of view updates for formally specified semantic data models based on the category theoretic sketch data model, and proves that in a variety of circumstances updatability is guaranteed independently of the current model.Expand

A program which facilitates storage and manipulation of finitely-presented (FP) categories and finite-set valued functors and several tools for testing properties of objects and arrows are included.Expand

Abstract This article shows that the distributive laws of Beck in the bicategory of sets and matrices, wherein monads are categories, determine strict factorization systems on their composite monads.… Expand

A variation on the lens concept called a c-lens is introduced, and shown to correspond to the categorical notion of Grothendieck opfibration, which guarantees a universal solution to the view update problem for functorial update processes.Expand

It is argued that the finite-limit, finite-sum sketches with a terminal node are the appropriate class and call them EA sketches, suitable for description of ERA models and their constraints.Expand