Yoneda structures on 2-categories

2-Categories and Yoneda lemma

Yoneda Structures from 2-toposes

A 2-categorical generalisation of the notion of elementary topos is provided, and some of the properties of the yoneda structure [SW78] it generates are explored. Results enabling one to exhibit objects as cocomplete in the sense definable within a yoneda structure are presented. Examples relevant to the globular approach to higher dimensional category theory are discussed. This paper also cont...

The Yoneda Lemma for unital A ∞ - categories

Let C be the differential graded category of differential graded k-modules. We prove that the Yoneda A∞-functor Y : A op → A∞(A,C) is a full embedding for an arbitrary unital A∞-category A. Since A∞-algebras were introduced by Stasheff [Sta63, II] there existed a possibility to consider A∞-generalizations of categories. It did not happen until A∞-categories were encountered in studies of mirror...

A∞-categories and the Yoneda lemma

Let C be the differential graded category of differential graded k-modules. We prove that the Yoneda A ∞ -functor Y : A → A ∞ (A,C) is a full embedding for an arbitrary unital A ∞ -category A. For a differential graded k-quiver B we define the free A ∞ -category FB generated by B. The main result is that the restriction A ∞ -functor A ∞ (FB,A) → A1(B,A) is an equivalence, where objects of the l...

Model Structures on pro - Categories

We introduce a notion of a ltered model structure and use this notion to produce various model structures on pro-categories. This framework generalizes the examples of [13], [15], and [16]. We give several examples, including a homotopy theory for G-spaces, where G is a pronite group. The class of weak equivalences is an approximation to the class of underlying weak