We study the existence and left properness of transferred model structures for “monoid-like”
objects in monoidal model categories. These include genuine monoids, but also all kinds of …

After a review of the concept of “monad with arities” we show that the category of algebras
for such a monad has a canonical dense generator. This is used to extend the …

The purpose of this paper is two-fold. In Part 1 we introduce a new theory of operadic
categories and their operads. This theory is, in our opinion, of an independent value. In Part …

Generalising Segal's approach to 1-fold loop spaces, the homotopy theory of n-fold loop
spaces is shown to be equivalent to the homotopy theory of reduced Θn-spaces, where Θn …

14 a prehistory of n-categorical physics just categories and bicategories). We also include a
review of some relevant aspects of twentieth-century physics. The most obvious roads to n …

The classical Eckmann–Hilton argument shows that two monoid structures on a set, such
that one is a homomorphism for the other, coincide and, moreover, the resulting monoid is …

Koszul duality is an important ingredient in the theory of algebraic operads. The classical
Koszul duality theory for associative algebras goes a long way back to Priddy [23], but a …

Abstract We construct A_ ∞ A∞ functors between Fukaya categories associated to
monotone Lagrangian correspondences between compact symplectic manifolds. We then …

What do dg-categories form? Page 1 Compositio Math. 143 (2007) 1335–1358 doi:10.1112/S0010437X07002771
What do dg-categories form? Dmitry Tamarkin Abstract We introduce a homotopy 2-category …

Operads are a powerful foundation for handling composition and substitution of various
structures. While at first the underlying combinatorics of operads concerned how trees are …