category theory

Definitions

A branch of mathematics which deals with spaces and maps between them in abstraction, taking similar theorems from various disparate more concrete branches of mathematics and unifying them.

uncountable

Equivalents

Examples

“Holonyms: math, maths, mathematics”

“As mentioned earlier set⟳ theory provides a general conceptual framework for mathematics. Now, since category theory, through the notion of topos, has succeeded in axiomatising set-theory, the outcome is an entirely new categorial foundation of mathematics! The category-theorists attitude that "function" rather than "set⟳ membership" can be seen as the fundamental mathematical concept has been entirely vindicated. The pre-eminent role of set⟳ theory in contemporary mathematics is suddenly challenged. A revolution has occurred in the history of mathematical ideas (albeit a peaceful one) that will undoubtedly influence⟳ the direction of the path to the future.”

“[Eugenia Cheng] We don't talk⟳ about this enough. We make⟳ choices about what to count⟳ as the same and what to count⟳ as different, and we should be aware that we're making them. [Katrina Miller:] What kind of math do you explore⟳ in the book? [Cheng 2025: Unequal: The Math of When Things Do and Don't Add⟳ Up] [Cheng:] Category theory is a branch of math with this radical idea that when you study⟳ things, you don’t have⟳ to know⟳ what they are. What you have⟳ to know⟳ is how they interact with other things. It's all about relationships rather than intrinsic characteristics. And one of the most important relationships is sameness and equivalence. When is a relationship good enough to count⟳ as things being the same? One of my favorite tongue-in-cheek examples is if you need⟳ to temporarily take⟳ over someone's role at work⟳ because they're on leave⟳. It typically doesn't matter⟳ what you look⟳ like⟳. Unless the work⟳ is being a body double⟳!”

CEFR level