In category theory, a strict 2-category is a category with "morphisms between morphisms", that is, where each hom-set itself carries the structure of a category. It can be formally defined as a …

A 2-category is called strict if all associators and unitors are identity 2-morphisms. A 2-category is called linear if all 2-morphism spaces C(aX b⇒ aY b) are finite dimensional complex vector …

The theory of Lie algebras can be categorified starting from a new notion of "2-vector space", which we define as an internal category in Vect. There is a 2-category 2Vect having these 2 …

Aug 8, 2024 · The notion of a 2-category generalizes that of category: a 2-category is a higher category, where on top of the objects and morphisms, there are also 2-morphisms. In old …

the category (Vec) of vector spaces any space of dimension zero. The colimit has the property that it has a unique map to every object and it is called an initial object. The empty set is an …

Sep 19, 2022 · Then the category you want is equivalent to the comma category $(F/G)$. To elaborate a bit, an object in $(F/G)$ is a pair of objects from the two source categories plus a …

In this paper we unfold the 2-category structure of the representations of a (strict) 2-group on (a suitable version of) Kapranov and Voevodsky’s 2-category of finite di-mensional 2-vector …

Example 6.1.4. There is a 2-category of topological spaces, continuous maps, and homotopy classes of homotopies between continuous maps. Examples 6.1.5. Here are some examples …

Mar 9, 2014 · As category theory describes set-like constructions, 2-category theory describes category-like constructions. You can usually build up categories with as objects sets with extra …

Jun 25, 2018 · The 2-category of 2-vector spaces has two monoidal structures $\boxtimes$ and $\boxplus$ where $\langle N\rangle\boxtimes \langle M\rangle = \langle N\cdot M\rangle$; the …