A mathematical model for cognitive structures and processes underlying innovations

TL;DR

This paper introduces a category theory-based mathematical model using presheaves to formally represent and analyze business innovations arising from combining features of existing systems, exemplified by the digital hub concept.

Contribution

It presents a novel formal framework employing presheaves to model and analyze innovative recombinations of systems across domains.

Findings

Framework successfully models the digital hub innovation

Provides formal tools for analyzing feature combinations

Bridges qualitative reasoning with mathematical rigor

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.