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# Open Diagrams via Coend Calculus (Román, 2020)

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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.

## # How to cite

  1 2 3 4 5 6 7 8 9 10 11 12 13  @inproceedings{openDiagrams, author = {Mario Rom{\'{a}}n}, editor = {David I. Spivak and Jamie Vicary}, title = {Open Diagrams via Coend Calculus}, booktitle = {Proceedings of the 3rd Annual International Applied Category Theory Conference 2020, {ACT} 2020, Cambridge, USA, 6-10th July 2020}, series = {{EPTCS}}, volume = {333}, pages = {65--78}, year = {2020}, doi = {10.4204/EPTCS.333.5}, }