The language of∞-categories provides an insightful new way of expressing many results in
higher-dimensional mathematics but can be challenging for the uninitiated. To explain what …

We set up a general theory of weak or homotopy-coherent enrichment in an arbitrary
monoidal∞-category. Our theory of enriched∞-categories has many desirable properties; …

String diagrams turn algebraic equations into topological moves that have recurring shapes,
involving the sliding of one diagram past another. We individuate, at the root of this fact, the …

We introduce simple models for associative algebras and bimodules in the context of
nonsymmetric∞–operads, and use these to construct an (∞, 2)–category of associative …

Optics are bidirectional data accessors that capture data transformation patterns such as
accessing subfields or iterating over containers. Profunctor optics are a particular choice of …

Reasoning about weak higher categorical structures constitutes a challenging task, even to
the experts. One principal reason is that the language of set theory is not invariant under the …

We introduce the notion of a relative pseudomonad, which generalizes the notion of a
pseudomonad, and define the Kleisli bicategory associated to a relative pseudomonad. We …

We universally characterize the produoidal category of monoidal lenses over a monoidal
category. In the same way that each category induces a cofree promonoidal category of …

We develop the theory of relative monads and relative adjunctions in a virtual equipment,
extending the theory of monads and adjunctions in a 2-category. The theory of relative …

This paper defines double fibrations (fibrations of double categories) and describes their key
examples and properties. In particular, it shows how double fibrations relate to existing …