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Τι (ποιος) είναι functorial topology - ορισμός

CONCEPT IN CATEGORY THEORY

Functorial point

Trivial topology

TOPOLOGY WHERE THE ONLY OPEN SETS ARE THE EMPTY SET AND THE ENTIRE SPACE

Indiscrete topology; Indiscrete space; Codiscrete topology

In topology, a topological space with the trivial topology is one where the only open sets are the empty set and the entire space. Such spaces are commonly called indiscrete, anti-discrete, concrete or codiscrete.

https://en.wikipedia.org/wiki/Trivial_topology

Computational topology

SUBFIELD OF TOPOLOGY WITH AN OVERLAP WITH AREAS OF COMPUTER SCIENCE

Algorithmic topology

Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular, computational geometry and computational complexity theory.

https://en.wikipedia.org/wiki/Computational_topology

Étale topology

GROTHENDIECK TOPOLOGY ON THE CATEGORY OF SCHEMES, WHOSE COVERING FAMILIES ARE JOINTLY SURJECTIVE FAMILIES OF ÉTALE MORPHISMS

Etale topology; Étale sheaf

In algebraic geometry, the étale topology is a Grothendieck topology on the category of schemes which has properties similar to the Euclidean topology, but unlike the Euclidean topology, it is also defined in positive characteristic. The étale topology was originally introduced by Grothendieck to define étale cohomology, and this is still the étale topology's most well-known use.

https://en.wikipedia.org/wiki/Étale_topology

Βικιπαίδεια

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. This idea often allows restating of definitions or properties of morphisms (such as monomorphism or product) given by a universal property in more familiar terms, by stating their relation to elements. Some very general theorems, such as Yoneda's lemma and the Mitchell embedding theorem, are of great utility for this, by allowing one to work in a context where these translations are valid. This approach to category theory – in particular the use of the Yoneda lemma in this way – is due to Grothendieck, and is often called the method of the functor of points.

https://en.wikipedia.org/wiki/Element (category theory)