...e subsets often do not); see [[#References|[a1]]], for example. In lattice theory, least upper bounds of directed subsets again play a distinctive part; see
[[Category:Order, lattices, ordered algebraic structures]]
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...ral transformations, the category of modules over $\Gamma$ is an [[Abelian category]], so one can do [[homological algebra]] with these objects.
...ilarly, equivariant local cohomology can be described using modules over a category depending on the space in question.
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[[Category:Linear and multilinear algebra; matrix theory]]
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...re all sets belonging to $U$, with morphisms and composition as above. The category of sets may be denoted by $\mathfrak S$, ENS, $\mathsf{Set}$ or Me.
...t every epimorphism is split is equivalent to the [[axiom of choice]]. The category of sets has a unique [[Bicategory(2)|bicategory]] (factorization) structure
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[[Category:Descriptive set theory]]
[[Category:Classical measure theory]]
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A [[category]] with an additional structure, thanks to which the internal Hom-functor ca
A category $\mathfrak{M}$ is said to be closed if a [[bifunctor]] $\otimes: \mathfrak{
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...}}(Y,X)$ defines a contravariant functor $h_X$ from $\mathcal{C}$ into the category of sets. For any object $F$ of $\hat{\mathcal{C}}$ there exists a natural b
...ieck functor it is possible to define algebraic structures on objects of a category (cf. [[Group object]]; [[Group scheme]]).
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[[Category:Number theory]]
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$#C+1 = 35 : ~/encyclopedia/old_files/data/M064/M.0604480 Modules, category of
The [[Category|category]] mod- $ R $
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[[Category:Number theory]]
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[[Category:Classical measure theory]]
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[[Category:Classical measure theory]]
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...pological vector space which is not a set of the [[Category of a set|first category]] is ultra-barrelled. If a [[locally convex space]] is ultra-barrelled, it
...gn="top">[1]</TD> <TD valign="top"> R.E. Edwards, "Functional analysis: theory and applications" , Holt, Rinehart & Winston (1965)</TD></TR>
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...system with multiple inputs and multiple outputs; see [[Automatic control theory]].
[[Category:Control theory and optimization]]
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...an 4 cannot, in general, be solved by radicals (see [[Galois theory|Galois theory]]).
...Many questions of the theory of radicals have been studied within category theory. See also [[Radical of a group|Radical of a group]]; [[Radical in a class o
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...lexes or simplicial decompositions. Simplicial spaces are the objects of a category whose morphisms $X\to Y$ are mappings such that every simplex of the triang
...gical spaces (cf. [[Simplicial object in a category|Simplicial object in a category]]).
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[[Category:Descriptive set theory]]
[[Category:Classical measure theory]]
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...s, the exponential law makes the [[category of sets]] a [[Cartesian-closed category]].
* Benjamin C. Pierce, ''Basic Category Theory for Computer Scientists'', MIT Press (1991) {{ISBN|0262660717}}
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[[Category:Group theory and generalizations]]
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...kernel of a homomorphism of groups, rings, etc. Let $\mathfrak{K}$ be a [[category]] with zero or [[null morphism]]s. A morphism $\mu : K \to A$ is called a k
...$ contains a null object (cf. [[Null object of a category|Null object of a category]]).
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