### Abstract

I consider the role of diagrams in contemporary mathematics. More specifically the role of certain diagrams—so-called directed graphs—will be investigated. I propose that these graphs act as mediating objects. This means that they link certain objects, that is, a C*-algebra and its associated K-groups, and that this link yields an epistemic gain. I explain that the link is possible because a graph represents as a metaphor in two distinct ways. In addition, the diagrammatic presentation of a directed graph becomes an object that can be manipulated. As such, it becomes what I will denote a “faithful representation.” The notion of a faithful representation tries to capture the fruitfulness of the combination of metaphorical representation with the possibility of controlled manipulation.

Original language | English |
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Journal | Endeavour |

Volume | 42 |

Issue number | 2-3 |

Pages (from-to) | 180-188 |

ISSN | 0160-9327 |

DOIs | |

Publication status | Published - 1. Jun 2018 |

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### Keywords

- Diagrams in contemporary mathematics
- Faithful representations
- Fruitfulness
- Manipulations on signs
- Mediating objects
- Semiotics