Corpus ID: 119618908

Regular patterns, substitudes, Feynman categories and operads

@article{Batanin2015RegularPS,
  title={Regular patterns, substitudes, Feynman categories and operads},
  author={M. Batanin and Joachim Kock and Mark Weber},
  journal={arXiv: Category Theory},
  year={2015}
}
We show that the regular patterns of Getzler (2009) form a 2-category biequivalent to the 2-category of substitudes of Day and Street (2003), and that the Feynman categories of Kaufmann and Ward (2013) form a 2-category biequivalent to the 2-category of coloured operads (with invertible 2-cells). These biequivalences induce equivalences between the corresponding categories of algebras. There are three main ingredients in establishing these biequivalences. The first is a strictification theorem… Expand
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