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A mathematical model for cognitive structures and processes underlying innovations

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  • Jurgen Jost
  • Massimo Warglien

Abstract

Business innovations are often arising from new combinations of pre-existing systems into new ones, coherently assembling features from their sources. We propose an abstract mathematical concept from category theory, the presheaf, to efficiently represent such coherent feature combinations. Moreover, operations on presheaves will allow us to formally describe and analyze business innovations that arise from novel mergings of systems from different domains. Equipped with such tools we provide an example by analyzing a successful case of such type of recombinant innovation, the digital hub concept proposed by Steve Jobs. The example shows how our framework can be used to bring formal rigor while preserving a fundamentally qualitative reasoning style.

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  • Jurgen Jost & Massimo Warglien, 2024. "A mathematical model for cognitive structures and processes underlying innovations," Papers 2411.01347, arXiv.org.
    • Handle: RePEc:arx:papers:2411.01347
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    1. Giovanni Gavetti & Daniel A. Levinthal & Jan W. Rivkin, 2005. "Strategy making in novel and complex worlds: the power of analogy," Strategic Management Journal, Wiley Blackwell, vol. 26(8), pages 691-712, August.
    2. Daniel Levinthal, 2006. "The Neo-Schumpeterian theory of the firm and the strategy field," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 15(2), pages 391-394, April.
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