Abstract
Many texts on Category Theory are written in a very terse style, in which it is assumed (a) that all relevant concepts are visualizable in diagrams and (b) that the texts’ readers can abductively reconstruct the diagrams that the authors had in mind based on no more than the most essential cues. In fact, there are many tacit conventions for drawing diagrams scattered through the literature, but a single unified diagrammatic language for all expository and interpretative contexts does not exist. This chapter offers an attempt to reconstruct abductively an (imaginary) language for missing diagrams: it proposes an extensible diagrammatic language, called DL, that follows the conventions of the diagrams in the literature whenever possible and that seems to be adequate for drawing “missing diagrams” for Category Theory. Examples include the “missing diagrams” for adjunctions and for the Yoneda Lemma. It is also shown how to formalize such abductive inferences of the missing diagrams in Agda.
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Ochs, E. (2022). On the Missing Diagrams in Category Theory. In: Magnani, L. (eds) Handbook of Abductive Cognition. Springer, Cham. https://doi.org/10.1007/978-3-030-68436-5_41-1
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DOI: https://doi.org/10.1007/978-3-030-68436-5_41-1
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