Mathematics > Category Theory
[Submitted on 9 Apr 2020 (v1), revised 26 Jan 2021 (this version, v4), latest version 21 Feb 2022 (v5)]
Title:Open Diagrams via Coend Calculus
View PDFAbstract:Morphisms in a monoidal category are usually interpreted as processes, and graphically depicted as square boxes. In practice, we are faced with the problem of interpreting what non-square boxes ought to represent in terms of the monoidal category and, more importantly, how should they be composed. Examples of this situation include lenses or learners. We propose a description of these non-square boxes, which we call open diagrams, using the monoidal bicategory of profunctors. A graphical coend calculus can then be used to reason about open diagrams and their compositions.
Submission history
From: EPTCS [view email] [via EPTCS proxy][v1] Thu, 9 Apr 2020 13:15:06 UTC (424 KB)
[v2] Mon, 27 Apr 2020 12:55:34 UTC (485 KB)
[v3] Tue, 12 May 2020 13:45:34 UTC (183 KB)
[v4] Tue, 26 Jan 2021 00:02:44 UTC (163 KB)
[v5] Mon, 21 Feb 2022 16:15:30 UTC (185 KB)
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