Open Diagrams via Coend Calculus
arXiv:2004.04526 · doi:10.4204/EPTCS.333.5
Abstract
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.
arXiv commentFormatting revision after Proceedings ACT 2020, minor changes
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- Cornering Optics
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- Collages of String Diagrams
- Optics for Premonoidal Categories
- A dataflow programming framework for linear optical distributed quantum computing
- Combs, Causality and Contractions in Atomic Markov Categories
- A Profunctorial Semantics for Quantum Supermaps