Factorization algebras are local-to-global objects that play a role in classical and quantum
field theory that is similar to the role of sheaves in geometry: they conveniently organize …

The notions of a post-group and a pre-group are introduced as a unification and enrichment
of several group structures appearing in diverse areas from numerical integration to the …

Although it has been a well-known fact, for more than two decades, that category theory is
needed for the study of topological orders, it is still a non-trivial challenge for students and …

We apply the mechanism of factorization homology to construct and compute category‐
valued two‐dimensional topological field theories associated to braided tensor categories …

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 …

The subject of this book is the theory of operads and colored operads, sometimes called
symmetric multicategories. A (colored) operad is an abstract object which encodes …

Rational homotopy theory is a branch of topology which studies the “non-torsion” behaviour
of the homotopy type of topological spaces. This area was born about fifty years ago in …

These notes are an expanded version of two series of lectures given at the winter school in
mathematical physics at les Houches and at the Vietnamese Institute for Mathematical …

We express the rational homotopy type of the mapping spaces $\mathrm {Map}^ h (\mathsf
D_m,\mathsf D_n^{\mathbb Q}) $ of the little discs operads in terms of graph complexes …

We study the question of dualizability in higher Morita categories of locally presentable
tensor categories and braided tensor categories. Our main results are that the 3-category of …