Marcy Robertson

On the Category of Props

The category of (colored) props is an enhancement of the category of colored operads, and thus of the category of small categories. The titular category has nice formal properties: it is bicomplete and is a symmetric monoidal category, with monoidal product closely related to the Boardman-Vogt tensor product of operads. Tools developed in this article, which is the first part of a larger work, include a generalized version of multilinearity of functors, a free prop construction defined on certain “generalized” graphs, and the relationship between the category of props and the categories of permutative categories and of operads.

The homotopy theory of simplicial props

The category of (colored) props is an enhancement of the category of colored operads, and thus of the category of small categories. In this paper, the second in a series on ‘higher props,’ we show that the category of all small colored simplicial props admits a cofibrantly generated model category structure. With this model structure, the forgetful functor from props to operads is a right Quillen functor.

Relative left properness of colored operads

The category of

Infinity properads and infinity wheeled properads

mathfrak{C}

Lecture Notes on Infinity-Properads

-colored symmetric operads admits a cofibrantly generated model category structure. In this paper, we show that this model structure satisfies a relative left properness condition, i.e., that the class of weak equivalences between

Fundamental Properads of Infinity Properads

Sigma

Wheeled Properads and Graphical Wheeled Properads

-cofibrant operads is closed under cobase change along cofibrations. We also provide an example of Dwyer which shows that the model structure on

Symmetric Monoidal Closed Structure on Properads

mathfrak{C}

Properadic Graphical Category

-colored symmetric operads is not left proper.

Properadic Graphical Sets and Infinity Properads

Introduction.- Graphs.- Properads.- Symmetric Monoidal Closed Structure on Properads.- Graphical Properads.- Properadic Graphical Category.- Properadic Graphical Sets and Infinity Properads.- Fundamental Properads of Infinity Properads.- Wheeled Properads and Graphical Wheeled Properads.- Infinity Wheeled Properads.- Whats Next?.