Abstract
In this paper, we argue that category theory (CT), the mathematical theory of abstract processes, could provide a concrete formal foundation for the study and practice of systems engineering. To provide some evidence for this claim, we trace the classic V-model of systems engineering, stopping along the way to (a) introduce elements of CT and (b) show how these might apply in a variety of systems engineering contexts.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abran A, Moore JW, Bourque P, Dupuise R, Tripp LL (2004) Software engineering body of knowledge. IEEE Computer Society, New York
Arbib M, Manes G (1974) Foundations of system theory: decomposable systems. Automatica 10(3):285–302
Arp R, Smith B, Spear AD (2015) Building ontologies with basic formal ontology. MIT Press, Cambridge
Baez J, Stay M (2011) Physics, topology, logic and computation: a Rosetta stone. In: Coecke B (ed) New structures for physics. Springer, Heidelberg, pp 95–168
Baez J, Fong B (2015) A compositional framework for passive linear networks. arXiv preprint 2015:1504.05625
Breiner S, Subrahmanian E, Jones A (2016) Categorical models for process planning. Under review: Computers and Industry
Coecke B, Fritz T, Spekkens RW (2014) A mathematical theory of resources. Inf Comput 250:59–86
Culbertson J, Sturtz K (2013) Bayesian machine learning via category theory. arXiv preprint 2013:1312.1445
Diskin Z (2008) Algebraic models for bidirectional model synchronization. In: Czarnecki K et al (eds) International conference on model driven engineering languages and systems. Springer, Berlin, pp 21–36
Diskin Z, Maibaum T (2014) Category theory and model-driven engineering: from formal semantics to design patterns and beyond. In: Cretu LG, Dumitriu F (eds) Model-driven engineering of information systems: principles, techniques, and practice. Apple, Toronto, pp 173–206
Eilenberg S, Mac LS (1945) General theory of natural equivalences. Trans Am Math Soc 58(2):231–294
Jacobs B (1999) Categorical logic and type theory. Elsevier, New York
Johnson M, Rosebrugh R, Wood RJ (2012) Lenses, brations and universal translations. Math Struct Comput Sci 22(01):25–42
Johnson M, Rosebrugh R, Wood RJ (2002) Entity-relationship-attribute designs and sketches. Theory Appl Categ 10(3):94–112
Lawvere FW (1986) Taking categories seriously. Revista Colombiana de Matematicas XX:147–178
Lawvere FW, Schanuel SH (2009) Conceptual mathematics: a first introduction to categories. Cambridge University Press, Cambridge
MacLane S, Moerdijk I (2012) Sheaves in geometry and logic: a first introduction to topos theory. Springer Science & Business Media, New York
Robinson M (2016). Sheaves are the canonical data structure for sensor integration. arXiv preprint 2016:1603.01446
Rosebrugh R, Wood RJ (1992) Relational databases and indexed categories. In: Seely RAG (ed) Proceedings of the International Category Theory Meeting 1991, vol 13. Canadian Mathematical Society, Providence, pp 391–407
Spivak DI (2012) Functorial data migration. Inf Comput 217:31–51
Spivak DI (2013) The operad of wiring diagrams: formalizing a graphical language for databases, recursion, and plug-and-play circuits. arXiv preprint 2013:1305.0297
Spivak DI (2014) Category theory for the sciences. MIT Press, Cambridge
Spivak DI, Kent RE (2012) Ologs: a categorical framework for knowledge representation. PLoS One 7(1):e24274
Spivak DI, Vasilakopoulou C, Schultz P (2016). Dynamical systems and sheaves. arXiv preprint 2016:1609.08086
Wisnesky R, Breiner S, Jones A, Spivak DI, Subrahmanian E (In press) Using category theory to facilitate multiple manufacturing service database integration. J Comput Inf Sci Eng
Disclaimer
Any mention of commercial products within NIST web pages is for information only; it does not imply recommendation or endorsement by NIST.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Breiner, S., Subrahmanian, E., Jones, A. (2018). Categorical Foundations for System Engineering. In: Madni, A., Boehm, B., Ghanem, R., Erwin, D., Wheaton, M. (eds) Disciplinary Convergence in Systems Engineering Research. Springer, Cham. https://doi.org/10.1007/978-3-319-62217-0_32
Download citation
DOI: https://doi.org/10.1007/978-3-319-62217-0_32
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-62216-3
Online ISBN: 978-3-319-62217-0
eBook Packages: EngineeringEngineering (R0)