Lesson plan
Subobject
In category theory, a branch of mathematics, a subobject of an object A in a category is a monomorphism into A , “up to isomorphism”. In various categories of mathematical structures, this coincides with the standard notion of a substructure of the given type of structure. For example, subobjects correspond to subsets in the category of sets, to subgroups in the category of groups, to subrings in the category of rings, etc. The dual concept to a subobject is a . This generalizes concepts such as quotient sets, quotient groups, quotient rings, etc.
Article summary
In category theory, a branch of mathematics, a subobject of an object A in a category is a monomorphism into A , “up to isomorphism”. In various categories of mathematical structures, this coincides with the standard notion of a substructure of the given type of structure. For example, subobjects correspond to subsets in the category of sets, to subgroups in the category of groups, to subrings in the category of rings, etc. The dual concept to a subobject is a . This generalizes concepts such as quotient sets, quotient groups, quotient rings, etc.
Key claims
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.