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Coproduct and Empty product

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Coproduct and Empty product

Coproduct vs. Empty product

In category theory, the coproduct, or categorical sum, is a category-theoretic 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. In mathematics, an empty product, or nullary product, is the result of multiplying no factors.

Similarities between Coproduct and Empty product

Coproduct and Empty product have 10 things in common (in Unionpedia): Cartesian product, Category of groups, Category of sets, Discrete category, Dual (category theory), Empty set, Initial and terminal objects, Limit (category theory), Product (category theory), Tuple.

Cartesian product

In set theory (and, usually, in other parts of mathematics), a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets.

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Category of groups

In mathematics, the category Grp has the class of all groups for objects and group homomorphisms for morphisms.

Category of groups and Coproduct · Category of groups and Empty product · See more »

Category of sets

In the mathematical field of category theory, the category of sets, denoted as Set, is the category whose objects are sets.

Category of sets and Coproduct · Category of sets and Empty product · See more »

Discrete category

In mathematics, in the field of category theory, a discrete category is a category whose only morphisms are the identity morphisms: Since by axioms, there is always the identity morphism between the same object, we can express the above as condition on the cardinality of the hom-set Some authors prefer a weaker notion, where a discrete category merely needs to be equivalent to such a category.

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Dual (category theory)

In category theory, a branch of mathematics, duality is a correspondence between the properties of a category C and the dual properties of the opposite category Cop.

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Empty set

In mathematics, and more specifically set theory, the empty set or null set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.

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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.

Coproduct and Initial and terminal objects · Empty product and Initial and terminal objects · See more »

Limit (category theory)

In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions such as products, pullbacks and inverse limits.

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Product (category theory)

In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas of mathematics such as the cartesian product of sets, the direct product of groups, the direct product of rings and the product of topological spaces.

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Tuple

In mathematics, a tuple is a finite ordered list (sequence) of elements.

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The list above answers the following questions

Coproduct and Empty product Comparison

Coproduct has 54 relations, while Empty product has 55. As they have in common 10, the Jaccard index is 9.17% = 10 / (54 + 55).

References

This article shows the relationship between Coproduct and Empty product. To access each article from which the information was extracted, please visit:

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