symmetric monoidal (∞,1)-category of spectra
internalization and categorical algebra
algebra object (associative, Lie, …)
An operadic category is a structure for describing various category-like structures (generalised operads) with different kinds of composition operations, including monoids, (symmetric and non-symmetric) operads, -operads, hyperoperads, and charades.
Every generalised operad has a notion of algebra, with which can be captured notions like (wheeled) properads, PROPs, cyclic operads, and (twisted) modular operads.
Operadic categories are thus a framework for generalised multicategories, albeit of a different style than approaches based on monads.
Michael Batanin and Martin Markl, Operadic categories and duoidal Deligne’s conjecture, Advances in Mathematics 285 (2015): 1630-1687, [arXiv:1404.3886].
Steve Lack, Operadic structures and their skew monoidal categories of collections, Higher Structures 2.1 (2018): 1-29, [arXiv:1610.06282].
Richard Garner, Joachim Kock, and Mark Weber, Operadic categories and décalage, Advances in Mathematics 377 (2021): 107440, [arXiv:1812.01750].
Michael Batanin and Martin Markl, Operadic categories as a natural environment for Koszul duality, Compositionality 5 (2023), [arXiv:1812.02935].
Last revised on January 29, 2026 at 09:20:54. See the history of this page for a list of all contributions to it.