Category theory

2017-07-27T23:26:19+03:00[Europe/Moscow] en true Grothendieck topology, Element (category theory), Direct limit, Category theory, Monoid, Preorder, Sheaf (mathematics), Isomorphism, Monoidal category, Natural transformation, Ringed space, Monad (category theory), Categorical algebra, Category algebra flashcards Category theory
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  • Grothendieck topology
    In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C which makes the objects of C act like the open sets of a topological space.
  • Element (category theory)
    In category theory, the concept of an element, or a point, generalizes the more usual set theoretic concept of an element of a set to an object of any category.
  • Direct limit
    In mathematics, a direct limit (also called inductive limit) is a colimit of a "directed family of objects".
  • Category theory
    Category theory formalizes mathematical structure and its concepts in terms of a collection of objects and of arrows (also called morphisms).
  • Monoid
    In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single associative binary operation and an identity element.
  • Preorder
    In mathematics, especially in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive.
  • Sheaf (mathematics)
    In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space.
  • Isomorphism
    In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism or morphism (i.e. a mathematical mapping) that admits an inverse.
  • Monoidal category
    In mathematics, a monoidal category (or tensor category) is a category C equipped with a bifunctor ⊗ : C × C → C which is associative up to a natural isomorphism, and an object I which is both a left and right identity for ⊗, again up to a natural isomorphism.
  • 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.
  • Ringed space
    In mathematics, a ringed space can be equivalently thought of either (a) a space together with a collection of commutative rings, the elements of which are "functions" on each open set of the space.
  • Monad (category theory)
    In category theory, a branch of mathematics, a monad (also triple, triad, standard construction and fundamental construction) is an endofunctor (a functor mapping a category to itself), together with two natural transformations.
  • Categorical algebra
    In mathematics, categorical algebra is a subfield of algebra that approaches algebra from the categorical point of view.
  • Category algebra
    In category theory, a field of mathematics, a category algebra is an associative algebra, defined for any locally finite category and commutative ring with unity.