Limit (category theory) (13422 bytes)
1: ...roduct (category theory)|products]] and [[inverse limit]]s.
2: ...sjoint union]]s and [[direct sum]]s. Limits and colimits have strong relationships to the categorial conc...
6: Before defining limits, it is useful to define the auxiliary notion of
21: A ''limit'' of a functor is just a ''universal cone''. In d...
22: ...ub>) of a functor ''F'' : ''J'' → ''C'' is a limit of that functor [[iff]]

Limit-preserving function (order theory) (8284 bytes)
1: ...he domain, then one obtains functions that are '''limit-reflecting'''.
7: ...per bound and a greatest lower bound. In [[domain theory]], on the other hand, one focuses on partially or...
9: ...t the supremum/infimum of their images. In domain theory, one often deals with so-called [[Scott-continuou...
11: ...'' [[functor]]s is in complete harmony with order theory, since orders can be considered as small categori...
18: ...sponds to the abovementioned parallel to category theory, but is not always required in the literature. In...

Category theory (21045 bytes)
1: ...es not mean that mathematicians consider category theory to be fuzzy or non-rigorous, merely that a small ...
3: See [[list of category theory topics]] for a breakdown of relevant articles.
7: ...other category and to every morphism in the first category a morphism in the second. Very commonly, certain ...
9: ...ds on a map are analagous to the morphisms of the category. Just as some roads are more important than othe...
13: ...an intuitive and geometric concept) to [[homology theory]], an [[axiom]]atic approach. It has been claimed...

Dual (category theory) (2592 bytes)
1: In [[category theory]], an abstract branch of [[mathematics]],
2: ... The dual category is also called the '''opposite category'''.
10: ...r example, if we take the opposite of a [[lattice theory|lattice]], we will find that ''meets'' and ''join...
12: ...iately useful, when one can identify the opposite category in concrete terms.
13: ... function]]s is equivalent to the opposite of the category of [[Boolean algebra]]s and homomorphisms.

Stack (category theory) (1937 bytes)
3: ...se to the notion of a stack as a certain kind of "category fibered in [[groupoid]]s".
14: [[Category:Category theory]][[Category:Algebraic geometry]]

Image (category theory) (644 bytes)
1: Given a [[category]] ''C'' and a [[morphism]] <math>f:X\rightarrow Y...
13: [[Category:Category theory]]

Connected (category theory) (310 bytes)
1: ...orphism]]s between two or more [[object (category theory)|objects]].
8: [[Category:Category theory]]

Pushout (category theory) (371 bytes)
1: ... of [[mathematics]], the '''pushout''' is the [[colimit]] of a diagram consisting of two [[morphism]]s ''...
3: ...y)|categorical dual]] of the [[pullback (category theory)|pullback]].
7: [[Category:Category theory]]

Product (category theory) (3687 bytes)
1: In [[category theory]], one defines '''products''' to generalize const...
3: Let ''C'' be a category and let {''X_i'' | ''i'' &isin; ''I''} ...
7: ... the limit of any [[discrete category|discrete subcategory]] in ''C''. Not every family {''X''<sub>''i''</su...
23: * [[Coproduct]] &ndash; the [[Dual (category theory)|dual]] of the product
24: * [[Limit (category theory)|Limit and colimits]]

Pullback (category theory) (2178 bytes)
1: ...er product''') is the [[limit (category theory)|limit]] of a diagram consisting of two [[morphism]]s ''...
15: ...tation comes from the following example. In the [[category of sets]] the pullback of ''f'' and ''g'' is the ...
19: ...ojections. This shows that pullbacks exist in any category with binary products and equalizers.
21: ...f a pullback is a called a '''[[pushout (category theory)|pushout]]'''.
26: [[Category:Category theory]]

Monad (category theory) (7318 bytes)
1: ...al transformation]]s. Monads are important in the theory of pairs of [[adjoint functors]]. They are formal...
5: ...ation of ''F''o''G'', is discussed under the dual theory of '''comonads'''.
7: ... (mathematics)|groups]] to the [[category of sets|category '''Set''']] of sets. Then as ''F'' we can take th...
32: ...a priori'' to be connected to an adjunction) on a category.
34: If we specialize to the category arising from a [[partially ordered set]] (''P'', ...

Kernel (category theory) (6449 bytes)
1: In [[category theory]] and its applications to other branches of [[mat...
7: Let <b>C</b> be a [[category theory|category]].
8: In order to define a kernel in the general category-theoretical sense, <b>C</b> needs to have [[zero ...
22: Note that in many [[concrete category|concrete]] contexts, one would refer to the objec...
29: ...the category of [[group (algebra)|group]]s or the category of (left) [[module (mathematics)|modules]] over a...

Structure (category theory) (2571 bytes)
3: ...ppings respecting that structure. Starting with a category ''C'' given abstractly, the challenge is to infer...
5: ... in fact be approached in a number of ways, the ''category'' structure not being (quite) an algebraic struct...
9: ...by [[Cayley's theorem]]. The analogue in category theory is the [[Yoneda lemma]]. One concludes that knowl...
11: [[Category:Category theory]]

Descent (category theory) (4877 bytes)
1: ... it is a tribute to the efforts to use [[category theory]] to get round the alleged 'brutality' of imposin...
3: ...of [[David Mumford]] in his [[geometric invariant theory]] spectacularly mixed [[scheme (mathematics)|sche...
11: ...re indeed standard conditions in [[fiber bundle]] theory. One important application to note is ''change of...
15: To move towards the abstract theory we need to interpret the disjoint union of the X<...
17: ... with which we began. This then allows a category theory approach: what remains to do is to re-express the...

List of category theory topics (2539 bytes)
1: This is a '''list of [[category theory]] topics''', by Wikipedia page.
4: *[[Category of sets]]
5: **[[Concrete category]]
6: *[[Category of vector spaces]]
7: **[[Category of graded vector spaces]]

Limit superior and limit inferior (5206 bytes)
1: ...uperior''' of a [[sequence]] can be thought of as limiting bounds on the sequence.
3: The limit inferior (or '''lower limit''') of a sequence (''x''_''n'') is defi...
11: Similarly, the limit superior (or '''upper limit''') of (''x''_''n'') is defined as
20: ...is case every sequence has a limit superior and a limit inferior.
30: ...n (''x''_''n'') in [-&infin;,&infin;] [[limit (mathematics)|converges]] if and only if

Limit (607 bytes)
1: A '''limit''' can be:
3: * [[Limit (mathematics)]], including:
4: ** [[Limit of a function]]
5: ** [[Limit of a sequence]]
7: ** [[Limit (category theory)]]

No limit (158 bytes)
1: '''No limit''' may refer to:
3: #A song by [[2 Unlimited]], see [[No Limit]].
7: [[sv:No limit]]

No Limit (546 bytes)
1: ...etting (poker)]]. For the record label, see [[No Limit Records]]''
2: ...rst single from the album ''[[No Limits]]''. ''No Limit'' is one of the most well know [[eurodance]] song...
4: [[Category:1993 singles|No Limit]]
6: [[sv:No Limit]]

Eddington limit (909 bytes)
3: ...physics]], the '''Eddington Limit''' is a natural limit to the [[luminosity]] that can be radiated by sph...
5: ...e luminosity naturally decreases to the Eddington limit where gas is pushed inward again.
7: The Eddington limit is a function of the mass of the accreting object...

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