Titlebook: Infinity Properads and Infinity Wheeled Properads; Philip Hackney,Marcy Robertson,Donald Yau Book 2015 Springer International Publishing S

核心

0075-8434 natorics of graphs and graphs substitution.Analyses technica.The topic of this book sits at the interface of the theory of higher categories (in the guise of (∞,1)-categories) and the theory of properads. Properads are devices more general than operads and enable one to encode bialgebraic, rather th

被告

Graphse develop graph theoretical concepts that will be needed later to define coface and codegeneracy maps in the graphical categories for connected (wheeled-free) graphs. We give graph substitution characterization of each of these concepts.

Obliterate

Wheeled Properads and Graphical Wheeled Properadsare infinite. In the rest of this chapter, we discuss wheeled versions of coface maps, codegeneracy maps, and graphical maps, which are used to define the wheeled properadic graphical category .. Every wheeled properadic graphical map has a decomposition into codegeneracy maps followed by coface maps.

sparse

Introduction,ndamental properad of an .-properad is characterized in terms of homotopy classes of 1-dimensional elements. Using all connected graphs instead of connected wheel-free graphs, a parallel theory of .-wheeled properads is also developed.

Pepsin

Properadic Graphical Categorys do not exist for general properad maps between graphical properads. Finally, we show that the properadic graphical category admits the structure of a (dualizable) generalized Reedy category, in the sense of Berger and Moerdijk (Math. Z. .(3–4), 977–1004, 2011).

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Preserve

Symmetric Monoidal Closed Structure on Properadsn of the tensor product of two free properads in terms of the two generating sets. In particular, when the free properads are finitely generated, their tensor product is finitely presented. This is not immediately obvious from the definition because free properads are often infinite sets.

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