Categorical quotient information

In algebraic geometry, given a category C, a categorical quotient of an object X with action of a group G is a morphism π : X → Y {\displaystyle \pi :X\to...

obtains a projective GIT quotient (which is a quotient of the set of semistable points.) A GIT quotient is a categorical quotient of the locus of semistable...

An intelligence quotient (IQ) is a total score derived from a set of standardised tests or subtests designed to assess human intelligence. The abbreviation...

{\displaystyle G/H} is a geometric quotient. A GIT quotient may or may not be a geometric quotient: but both are categorical quotients, which is unique; in other...

Q} can then be thought of as a relative version of the Abel map. Categorical quotient, a special case One also needs to assume the geometric fibers are...

of (locally small) categories, analogous to a quotient group or quotient space, but in the categorical setting. Let C be a category. A congruence relation...

quotient object. This generalizes concepts such as quotient sets, quotient groups, quotient spaces, quotient graphs, etc. An appropriate categorical definition...

condition holds with < replaced by ≤. GIT quotient Geometric complexity theory Geometric quotient Categorical quotient Quantization commutes with reduction...

conveniently expressed and unified in terms of categories. Examples include quotient spaces, direct products, completion, and duality. Many areas of computer...

coequaliser) is a generalization of a quotient by an equivalence relation to objects in an arbitrary category. It is the categorical construction dual to the equalizer...

field of quotients, or quotient field of R {\displaystyle R} . All four are in common usage, but are not to be confused with the quotient of a ring by...

naturally homeomorphic. Categorically, Kolmogorov spaces are a reflective subcategory of topological spaces, and the Kolmogorov quotient is the reflector. Topological...

topological spaces using the techniques of category theory is known as categorical topology. N.B. Some authors use the name Top for the categories with...

practice of categorizing human intelligence, as measured by intelligence quotient (IQ) tests, into categories such as "superior" or "average". In the current...

In category theory, the coproduct, or categorical sum, is a construction which includes as examples the disjoint union of sets and of topological spaces...

that is both ω {\displaystyle \omega } -categorical and uncountably categorical is called totally categorical. A key factor in the structure of the class...

f\circ g_{1}=f\circ g_{2}\implies g_{1}=g_{2}.} Monomorphisms are a categorical generalization of injective functions (also called "one-to-one functions");...

a word in combinatorics or of a word in group theory. An independent categorical variable. In experimental design, the factor is a category of treatments...

x_{0}} and y 0 {\displaystyle y_{0}} ) the wedge sum of X and Y is the quotient space of the disjoint union of X and Y by the identification x 0 ∼ y 0...

limit and direct limit, kernels and cokernels, quotient groups, quotient vector spaces, and other quotient spaces. Before giving a formal definition of...

equivalence classes is an easy example of a theory which is ω-categorical, but not categorical for any larger cardinal number. An implication of model theory...

as a categorical product. But its k-ification k ( X × Y ) {\displaystyle k(X\times Y)} does belong to the expected category and is the categorical product...