# 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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Abstract An \algebraic left Kan extension" is a left Kan extension which interacts well with the alge- braic structure present in the given situation, and these appear in various subjects such as the… Expand