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The combinatorics of n-categorical pasting☆
- Michael Johnson
- 15 December 1989
Fibrations and universal view updatability
Lenses and Learners
This paper shows both that there is a faithful, identity-on-objects symmetric monoidal functor embedding a category of asymmetric lenses into the category of learners, and furthermore there is such a functorEmbedding the categories of learners into a categories of symmetric lenses.
Lenses, fibrations and universal translations†
- Michael Johnson, R. Rosebrugh, R. J. Wood
- MathematicsMathematical Structures in Computer Science
- 19 September 2011
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.
Entity-relationship-attribute designs and sketches
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.
View Updatability Based on the Models of a Formal Specification
This paper defines view updates by a universal property in a subcategory of models of the formal specification, and explains why this indeed gives a comprehensive treatment of view updatability, including a solution to the view update problem.
On the Value of Commutative Diagrams in Information Modelling
This paper shows how commutative diagrams have been used to develop new methodologies in ER-modelling, constraint specification and process modelling, and suggests new but as yet untested techniques for information model partitioning and information system architecture.
On category theory as a (meta) ontology for information systems research
The role of category theory as an ontological tool for information systems research is discussed and its use with anumber of examples including system specification, the definitions of views and view updates, and system interoperations are illustrated.
Spans of lenses
These functors which exhibit a category whose arrows are spans of wellbehaved lenses as a retract of a categorywhose arrows are the corresponding symmetric lenses are related to the asymmetric lenses of Hofmann, Pierce and Wagner.
Universal Arrow Foundations for Visual Modeling
The goal of the paper is to explicate some common formal logic underlying various notational systems used in visual modeling. The idea is to treat the notational diversity as the diversity of…