Faster access than browser!
22 relations: Accessible category, Adjoint functors, Cartesian closed category, Category (mathematics), Category theory, Complete category, Conglomerate (set theory), Exponential object, Forgetful functor, Free category, Functor, Functor category, Glossary of category theory, Initial and terminal objects, Mathematics, Morphism, Natural transformation, Nerve (category theory), Quasi-category, Quiver (mathematics), Russell's paradox, Strict 2-category.
Accessible category
The theory of accessible categories is a part of mathematics, specifically of category theory.
New!!: Category of small categories and Accessible category · See more »
Adjoint functors
In mathematics, specifically category theory, adjunction is a possible relationship between two functors.
New!!: Category of small categories and Adjoint functors · See more »
Cartesian closed category
In category theory, a category is considered Cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors.
New!!: Category of small categories and Cartesian closed category · See more »
Category (mathematics)
In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is an algebraic structure similar to a group but without requiring inverse or closure properties.
New!!: Category of small categories and Category (mathematics) · See more »
Category theory
Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).
New!!: Category of small categories and Category theory · See more »
Complete category
In mathematics, a complete category is a category in which all small limits exist.
New!!: Category of small categories and Complete category · See more »
Conglomerate (set theory)
In mathematics, a conglomerate is a collection of classes, just as a class is a collection of sets.
New!!: Category of small categories and Conglomerate (set theory) · See more »
Exponential object
In mathematics, specifically in category theory, an exponential object or map object is the categorical generalization of a function space in set theory.
New!!: Category of small categories and Exponential object · See more »
Forgetful functor
In mathematics, in the area of category theory, a forgetful functor (also known as a stripping functor) 'forgets' or drops some or all of the input's structure or properties 'before' mapping to the output.
New!!: Category of small categories and Forgetful functor · See more »
Free category
In mathematics, the free category or path category generated by a directed graph or quiver is the category that results from freely concatenating arrows together, whenever the target of one arrow is the source of the next.
New!!: Category of small categories and Free category · See more »
Functor
In mathematics, a functor is a map between categories.
New!!: Category of small categories and Functor · See more »
Functor category
In category theory, a branch of mathematics, the functors between two given categories form a category, where the objects are the functors and the morphisms are natural transformations between the functors.
New!!: Category of small categories and Functor category · See more »
Glossary of category theory
This is a glossary of properties and concepts in category theory in mathematics.
New!!: Category of small categories and Glossary of category theory · See more »
Initial and terminal objects
In category theory, a branch of mathematics, an initial object of a category C is an object I in C such that for every object X in C, there exists precisely one morphism I → X. The dual notion is that of a terminal object (also called terminal element): T is terminal if for every object X in C there exists a single morphism X → T. Initial objects are also called coterminal or universal, and terminal objects are also called final.
New!!: Category of small categories and Initial and terminal objects · See more »
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
New!!: Category of small categories and Mathematics · See more »
Morphism
In mathematics, a morphism is a structure-preserving map from one mathematical structure to another one of the same type.
New!!: Category of small categories and Morphism · See more »
Natural transformation
In category theory, a branch of mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal structure (i.e., the composition of morphisms) of the categories involved.
New!!: Category of small categories and Natural transformation · See more »
Nerve (category theory)
In category theory, a discipline within mathematics, the nerve N(C) of a small category C is a simplicial set constructed from the objects and morphisms of C. The geometric realization of this simplicial set is a topological space, called the classifying space of the category C. These closely related objects can provide information about some familiar and useful categories using algebraic topology, most often homotopy theory.
New!!: Category of small categories and Nerve (category theory) · See more »
Quasi-category
In mathematics, more specifically category theory, a quasi-category (also called quasicategory, weak Kan complex, inner Kan complex, infinity category, ∞-category, Boardman complex, quategory) is a generalization of the notion of a category.
New!!: Category of small categories and Quasi-category · See more »
Quiver (mathematics)
In mathematics, a quiver is a directed graph where loops and multiple arrows between two vertices are allowed, i.e. a multidigraph.
New!!: Category of small categories and Quiver (mathematics) · See more »
Russell's paradox
In the foundations of mathematics, Russell's paradox (also known as Russell's antinomy), discovered by Bertrand Russell in 1901, showed that some attempted formalizations of the naïve set theory created by Georg Cantor led to a contradiction.
New!!: Category of small categories and Russell's paradox · See more »
Strict 2-category
In category theory, a strict 2-category is a category with "morphisms between morphisms", that is, where each hom-set itself carries the structure of a category.
New!!: Category of small categories and Strict 2-category · See more »
Redirects here:
Category of all categories, Category of all small categories, Category of categories, Empty category (category theory), Terminal category, Trivial category.
References
[1] https://en.wikipedia.org/wiki/Category_of_small_categories
