**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Concept# Subobject

Summary

In , a branch of mathematics, a subobject is, roughly speaking, an that sits inside another object in the same . The notion is a generalization of concepts such as subsets from set theory, subgroups from group theory, and subspaces from topology. Since the detailed structure of objects is immaterial in category theory, the definition of subobject relies on a morphism that describes how one object sits inside another, rather than relying on the use of elements.
The concept to a subobject is a . This generalizes concepts such as quotient sets, quotient groups, quotient spaces, quotient graphs, etc.
Definitions
An appropriate categorical definition of "subobject" may vary with context, depending on the goal. One common definition is as follows.
In detail, let A be an object of some category. Given two monomorphisms
:u: S \to A \ \text{and} \ v: T\to A
with codomain A, we define an equivalence relation by u \equiv v if

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading

Related publications

Related people

No results

No results

Related units

Related courses

No results

No results

Related lectures

Related concepts

No results

No results