We study polynomial functors over locally cartesian closed categories. After setting up the
basic theory, we show how polynomial functors assemble into a double category, in fact a …

Operads may be represented as symmetric monoidal functors on a small symmetric
monoidal category. We discuss the axioms which must be imposed on a symmetric …

We introduce a general theory of parametrized objects in the setting of ß–categories.
Although parametrised spaces and spectra are the most familiar examples, we establish our …

For N∞ operads O and O such that there is an inclusion of the associated indexing systems,
there is a forgetful functor from incomplete Tambara functors over O to incomplete Tambara …

We give a Quillen equivalence between May and Sigurdsson's model category of
parametrized spectra over BG, and Mandell, May, Schwede, and Shipley's model category …

Category theory provides structure for the mathematical world and is seen everywhere in
modern mathematics. With this book, the author bridges the gap between pure category …

The settings for homotopical algebra—categories such as simplicial groups, simplicial rings,
A∞ spaces, E∞ ring spectra, etc.—are often equivalent to categories of algebras over some …

In this paper we study the homotopy theory of parameterized spectrum objects in the∞-
category of (∞, 2)-categories, as well as the Quillen cohomology of an (∞, 2)-category with …

The category of small covariant functors from simplicial sets to simplicial sets supports the
projective model structure [B. Chorny, WG Dwyer, Homotopy theory of small diagrams over …

B ́enabou pointed out in 1963 that a pair f⊣ u: A→ B of adjoint functors induces a monoidal
functor [f, u]:[A, A]→[B, B] between the (strict) monoidal categories of endofunctors. We show …