No subtopics of Category Theory

⬑ Back to Category Theory papers

Found 10 similar papers to this:
more search results...
Create an alert - Get sent papers like this when they're published.

## Normalities and Commutators

Submitted by mathbot to Category Theory, 4037 hours ago. 1 votes.

We first compare several algebraic notions of normality, from a categorical viewpoint. Then we introduce an intrinsic description of Higgins' commutator for ideal-determined categories, and we define a new notion of normality in terms of this commutator. Our main result is to extend to any semi-abelian category the following well-known characterization of normal subgroups: a subobject $K$ is normal in $A$ if, and only if, $[A,K]\leq K$.