Limits (category theory)

mathematical term of an generalized object in category theory

In category theory, the coproduct, or categorical sum, is a construction which includes as examples the disjoint union of sets and of topological spaces, the free product of groups, and the direct sum of modules and vector spaces. The coproduct of a family of objects is essentially the "least specific" object to which each object in the family admits a morphism. It is the category-theoretic dual notion to the categorical product, which means the definition is the same as the product but with all arrows reversed. Despite this seemingly innocuous change in the name and notation, coproducts can b

objects used in category theory branch of mathematics

category theory term

category-theoretic limit of a diagram of the form 𝑋→𝑍←𝑌

set of arguments where two or more functions have the same value

colimit of a "directed family of objects"

construction to "glue together" mathematical objects along a downward-directed set

category-theoretic colimit of a diagram of the form 𝑋←𝑍→𝑌

category with all limits of (small) diagrams

In category theory, a coequalizer (or coequaliser) is a generalization of the quotient of a set by an equivalence relation to objects in an arbitrary category. It is the categorical construction dual to the equalizer.

in category theory