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The following is a brief summary (with examples) of what category theory is.


Category theory studies mathematical structure: categories of objects (intentionally undefined, but could be a set, topological space, groups, or anything else) and the mappings of those objects between categories (morphisms). 

You can think of morphisms as the “arrow” that maps between categories. Morphisms can be functions (but don’t have to be) and might be composed (similar to functions). 

Category theory is abstract enough to be applied to many concepts outside mathematics. Here are a few examples:

Some examples:

For more in-depth examples and analysis (yet still accessible), there’s Category Theory for Programmers.

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