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searching for Category of rings 10 found (77 total)

Cotriple homology (332 words) [view diff] exact match in snippet view article find links to article

_{R}N} . Let F be the left adjoint of the forgetful functor from the category of rings to Set; i.e., free module functor. Then F U {\displaystyle FU} defines

Hopfian object (842 words) [view diff] exact match in snippet view article find links to article

The situation in the category of rings is quite different from the category of modules. The morphisms in the category of rings with unity are required

Bivariant theory (433 words) [view diff] exact match in snippet view article find links to article

a contravariant functor from the category of (nice) spaces to the category of rings. A bivariant theory is a functor both covariant and contravariant;

Subobject (907 words) [view diff] exact match in snippet view article find links to article

all injective continuous functions are subspace embeddings. In the category of rings, the inclusion Z ↪ Q {\displaystyle \mathbb {Z} \hookrightarrow \mathbb

Forgetful functor (1,161 words) [view diff] exact match in snippet view article find links to article

binary operations. Deleting the 1 gives a forgetful functor to the category of rings without unit; it simply "forgets" the unit. Deleting × {\displaystyle

Realcompact space (382 words) [view diff] exact match in snippet view article find links to article

In particular the category of realcompact spaces is dual to the category of rings of the form C(X). In order that a Hausdorff space X is compact it

K-theory of a category (1,642 words) [view diff] exact match in snippet view article find links to article

functor from the category of rings to the category of abelian groups. The higher K-theory should then be a functor from the category of rings but to the category

Regular category (1,127 words) [view diff] exact match in snippet view article find links to article

elementary topos Grp, the category of groups and group homomorphisms The category of rings and ring homomorphisms More generally, the category of models of any

Field with one element (3,811 words) [view diff] exact match in snippet view article find links to article

notions by "gluing" the category of multiplicative monoids and the category of rings to create a new category M R , {\displaystyle {\mathfrak {M}}{\mathfrak

Isbell's zigzag theorem (1,751 words) [view diff] exact match in snippet view article find links to article

are absolutely closed. Example of non-surjective epimorphism in the category of rings: The inclusion i : ( Z , ⋅ ) ↪ ( Q , ⋅ ) {\displaystyle i:(\mathbb