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Comparison of the definitions of abelian (904).
| Content Provider | CiteSeerX |
|---|---|
| Abstract | Abstract. In the efforts to define a 2-categorical analog of an abelian category, two (or three) notions of “abelian 2-categories ” are defined in [4] and [2]. One is the relatively exact 2-category defined in [4], and the other(s) is the (2-)abelian Gpd-category defined by Dupont [2]. We compare these notions, using the arguments in [4] and [2]. Since they proceed independently in their own way, in different settings and terminologies, it will be worth while to collect and unify them. In this paper, by comparing their definitions and arguments, we show the relationship among these classes of 2-categories. 1. introduction Motiveted by [5], we defined a general class of 2-categories ‘relatively exact 2-categories ’ in [4] (originally written as our master’s thesis in 2006), so as to make the 2-categorical homological algebra work well in an abstract setting. A relatively exact 2-category is a generalization of SCG ( = the 2-category of symmetric categorical groups), and defined as a 2-categorical analog of an abelian category. |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Definition Abelian 2-categorical Analog Abelian Category Exact 2-categories Abelian Gpd-category Abstract Setting General Class Abelian 2-categories Different Setting Master Thesis 2-categorical Homological Algebra Work Symmetric Categorical Group |
| Content Type | Text |
| Resource Type | Article |
