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Category theory

Adjoint functors
Relationship between two functors abstracting many common constructions
Cartesian closed category
Type of category in category theory
Comma category
Mathematics construct
Commutative diagram
Collection of maps which give the same result
Concrete category
Category equipped with a faithful functor to the category of sets
Coproduct
Category-theoretic construction
Five lemma
Lemma in category theory about commutative diagrams
Forgetful functor
Drops some or all of the input's structure or properties
Free object
Value of a left adjoint functor to a forgetful functor
Functor
Mapping between categories in mathematical category theory
Hom functor
Functor mapping hom objects to an underlying category
Initial and terminal objects
Special objects used in (mathematical) category theory
Kan extension
Category theory constructs
Limit (category theory)
Terminology used in theoretical mathematics involving categories.
Monad (category theory)
Operation in algebra and mathematics
Morphism
Map (arrow) between two objects of a category
Natural transformation
Central object of study in category theory
Nine lemma
Category theory lemma about commutative diagrams
Opposite category
Category constructed from another category C, whose objects are the same as those of C, whose morphisms from X to Y are the same as the morphisms in C from Y to X
Product (category theory)
Generalized object in category theory
Pullback (category theory)
Most general completion of a commutative square given two morphisms with same codomain
Pushout (category theory)
Category-theoretic colimit of a diagram of the form 𝑋←𝑍→𝑌
Snake lemma
Tool used in mathematics
Subcategory
Category whose objects and morphisms are inside a bigger category
Universal property
Central object of study in category theory
Yoneda lemma
Theorem in category theory