The branch of mathematics which formalizes a number of algebraic properties of collections of transformations between mathematical objects (such as binary relations, groups, sets, topological spaces, etc.) of the same type, subject to the constraint that the collections contain the identity mapping and are closed with respect to compositions of mappings. The objects studied in category theory are called categories.

# Category Theory

## See also

Category## Explore with Wolfram|Alpha

## Cite this as:

Weisstein, Eric W. "Category Theory."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/CategoryTheory.html