Help


[permalink] [id link]
+
Page "Limit (category theory)" ¶ 61
from Wikipedia
Edit
Promote Demote Fragment Fix

Some Related Sentences

Given and diagram
Given two complexes M < sub >*</ sub > and N < sub >*</ sub >, a chain map between the two is a series of homomorphisms from M < sub > i </ sub > to N < sub > i </ sub > such that the entire diagram involving the boundary maps of M and N commutes.
Given a commutative diagram, a proof by diagram chasing involves the formal use of the properties of the diagram, such as injective or surjective maps, or exact sequences.
* Voronoi diagram: Given a set of points, partition the space according to which points are closest to the given points.
Given and, a morphism in the coslice category is a map making the following diagram commute:
Given a Dynkin diagram X, Chevalley constructed a group scheme over the integers Z whose values over finite fields are the Chevalley groups.
Given that PLCs usually control systems which are easily represented by a state transition diagram, the use of a very high-level programming language such as state logic greatly helps the PLC programmer in making intuitive control programs.

Given and F
Given a field F, the assertion “ F is algebraically closed ” is equivalent to other assertions:
Given the first n digits of Ω and a k ≤ n, the algorithm enumerates the domain of F until enough elements of the domain have been found so that the probability they represent is within 2 < sup >-( k + 1 )</ sup > of Ω.
Given any vector space V over a field F, the dual space V * is defined as the set of all linear maps ( linear functionals ).
Given a field ordering ≤ as in Def 1, the elements such that x ≥ 0 forms a positive cone of F. Conversely, given a positive cone P of F as in Def 2, one can associate a total ordering ≤< sub > P </ sub > by setting x ≤ y to mean y − x ∈ P. This total ordering ≤< sub > P </ sub > satisfies the properties of Def 1.
Given a class function G: V V, there exists a unique transfinite sequence F: Ord V ( where Ord is the class of all ordinals ) such that
Given a functor F: J C ( thought of as an object in C < sup > J </ sup >), the limit of F, if it exists, is nothing but a terminal morphism from Δ to F. Dually, the colimit of F is an initial morphism from F to Δ.
Given a natural transformation Φ from h < sup > A </ sup > to F, the corresponding element of F ( A ) is.
Given a topological space X, denote F the set of filters on X, x ∈ X a point, V ( x )F the neighborhood filter of x, A ∈ F a particular filter and the set of filters finer than A and that converge to x.
* Shay Given – former goalkeeper for both the Republic of Ireland and Newcastle United F. C ..
Given a topological space X, a base for the closed sets of X is a family of closed sets F such that any closed set A is an intersection of members of F.
Given any subset F =

Given and J
Given two fractional ideals I and J, one defines their product IJ as the set of all finite sums: the product IJ is again a fractional ideal.
Given a set S with three subsets, J, K, and L, the following holds:
Given a hermitian structure on a vector space, J and Ω are related via
Given that the degree specializes in international law, and is not teaching a first degree in U. S. law ( the J. D.
An identity involving four operators ( F, G, U, and V ) and a product operation (·) has been pointed out by L. J. Landau: Given that the following four pairs of operators commute:
Given the partition function Z in terms of the source field J, the energy functional is its logarithm.
* Kim T. J. A Combined Land Use-Transportation Model When Zonal Travel Demand is Endogenously Given, Transportation Research, 17B, pp. 449 – 462.
Given a symplectic form ω and a linear complex structure J, one may define an associated symmetric bilinear form g < sub > J </ sub > on V < sub > J </ sub >
* Given, Brian J.
Given the coefficient sequence for some M < J and all the difference sequences, k = M ,..., J-1, one computes recursively
Given Armstrong's concerns, the administration employed general counsel J. Patrick Abell to file a friendly test case to determine the constitutionality of the incentive package.
Given a high-profile spot on the all-star compilation Roll Wit tha Flava as their first recording opportunity, Zhane lived up to the pressure and came away with one of the hip-hop party anthems of all time, " Hey, Mr. D. J.
Given a simply connected and open subset D of R < sup > 2 </ sup > and two functions I and J which are continuous on D then an implicit first-order ordinary differential equation of the form
Given an arbitrary Riemannian metric g on an almost complex manifold M one can construct a new metric g ′ compatible with the almost complex structure J in an obvious manner:

Given and
* Given any Banach space X, the continuous linear operators A: X X form a unitary associative algebra ( using composition of operators as multiplication ); this is a Banach algebra.
Given a subset X of a manifold M and a subset Y of a manifold N, a function f: X Y is said to be smooth if for all p in X there is a neighborhood of p and a smooth function g: U N such that the restrictions agree ( note that g is an extension of f ).
* Given any set X, there is an equivalence relation over the set of all possible functions X X.
Given two groups G and H and a group homomorphism f: G H, let K be a normal subgroup in G and φ the natural surjective homomorphism G G / K ( where G / K is a quotient group ).
Given metric spaces ( X, d < sub > 1 </ sub >) and ( Y, d < sub > 2 </ sub >), a function f: X Y is called uniformly continuous if for every real number ε > 0 there exists δ > 0 such that for every x, y ∈ X with d < sub > 1 </ sub >( x, y ) < δ, we have that d < sub > 2 </ sub >( f ( x ), f ( y )) < ε.
Given a morphism f: B A the associated natural transformation is denoted Hom ( f ,–).
Given a function f: X Y, the set X is the domain of f ; the set Y is the codomain of f. In the expression f ( x ), x is the argument and f ( x ) is the value.
* Given a category C with finite coproducts, a cogroup object is an object G of C together with a " comultiplication " m: G G G, a " coidentity " e: G 0, and a " coinversion " inv: G G, which satisfy the dual versions of the axioms for group objects.
Given a subset S in R < sup > n </ sup >, a vector field is represented by a vector-valued function V: S R < sup > n </ sup > in standard Cartesian coordinates ( x < sub > 1 </ sub >, ..., x < sub > n </ sub >).
Given a vector x ∈ V and y * ∈ W *, then the tensor product y * ⊗ x corresponds to the map A: W V given by
: Given two sets, A and T, of equal size, together with a weight function C: A × T R. Find a bijection f: A T such that the cost function:
* Given any morphism k ′: K ′ X such that f k ′ is the zero morphism, there is a unique morphism u: K ′ K such that k u
Given a concrete category ( C, U ) and a cardinal number N, let U < sup > N </ sup > be the functor C Set determined by U < sup > N </ sup >( c ) = ( U ( c ))< sup > N </ sup >.

2.667 seconds.