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Sets for Mathematics
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 theExpand
GENERIC COMMUTATIVE SEPARABLE ALGEBRAS AND COSPANS OF GRAPHS
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 finiteExpand
THE SEPARATED EXTENSIONAL CHU CATEGORY
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 ∗-autonomousExpand
Constructive complete distributivity IV
TLDR
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
A basic distributive law
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 forExpand
Fibrations and universal view updatability
TLDR
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 database of categories
TLDR
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
Distributive laws and factorization
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
Lenses, fibrations and universal translations†
TLDR
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
Entity-relationship-attribute designs and sketches
TLDR
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
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