[permalink] [id link]
Given a presheaf, a natural question to ask is to what extent its sections over an open set U are specified by their restrictions to smaller open sets V < sub > i </ sub > of an open cover of U. A presheaf is separated if its sections are " locally determined ": whenever two sections over U coincide when restricted to each of V < sub > i </ sub >, the two sections are identical.
from
Wikipedia
Some Related Sentences
Given and natural
Given the small population of the region ( compared with the Central Canadian provinces or the New England states ), the regional economy is a net exporter of natural resources, manufactured goods, and services.
Given that a natural language such as English contains, at any given time, a finite number of words, any comprehensive list of definitions must either be circular or rely upon primitive notions.
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 that the coiled texture is the natural state of some African Americans ' hair, or perceived as being more " African ", this simple style is now often seen as a sign of self-acceptance and an affirmation that the beauty norms of the ( eurocentric ) dominant culture are not absolute.
Given an arbitrary group G, there is a related profinite group G < sup >^</ sup >, the profinite completion of G. It is defined as the inverse limit of the groups G / N, where N runs through the normal subgroups in G of finite index ( these normal subgroups are partially ordered by inclusion, which translates into an inverse system of natural homomorphisms between the quotients ).
Given that the authors were the primary developers of the Unix operating system, it is natural that QED had a strong influence on the classic UNIX text editors ed, sed and their descendants such as ex and sam.
Given a natural transformation Φ from h < sup > A </ sup > to F, the corresponding element of F ( A ) is.
Given a morphism f: B → A the associated natural transformation is denoted Hom ( f ,–).
Given a diagram F: J → C ( thought of as an object in C < sup > J </ sup >), a natural transformation ψ: Δ ( N ) → F ( which is just a morphism in the category C < sup > J </ sup >) is the same thing as a cone from N to F. The components of ψ are the morphisms ψ < sub > X </ sub >: N → F ( X ).
Given his socialist agenda in Egypt, the Ba ' ath should have been his natural ally, but Nasser was hesitant to share power.
Given the reputed humorous character of Valencians, it was natural that they began to burn figurines depicting people and events of the past year.
Given a stochastic process, the natural filtration for ( or induced by ) this process is the filtration where is generated by all values of up to time s
Given this natural tendency to glide forward, terza rima is especially well-suited to narration and description ".
Given this, it is quite natural and convenient to designate a general sequence a < sub > n </ sub > by by the formal expression, even though the latter is not an expression formed by the operations of addition and multiplication defined above ( from which only finite sums can be constructed ).
Given a series with values in a normed abelian group G and a permutation σ of the natural numbers, one builds a new series, said to be a rearrangement of the original series.
Given a natural number x, h outputs the index of the partial computable function that performs the following computation:
Given its central location, Athlone is a natural hub for transport, with frequent bus and rail schedules.
Given the finite supply of natural resources at any specific cost and location, agriculture that is inefficient or damaging to needed resources may eventually exhaust the available resources or the ability to afford and acquire them.
Given this difference, it is necessary that logistic regression take the natural logarithm of the odds ( referred to as the logit or log-odds ) to create a continuous criterion.
Given that the logit is not generally interpreted and that the inverse of the natural logarithm, the exponential function of the logit is generally interpreted instead, it is also helpful to examine this function ( denoted: ).
Given that some countries now ban docking, breeders are again attempting to select dogs with the genes for natural bob tails.
Given such a G-module M, it is natural to consider the subgroup of G-invariant elements:
Given its native distribution the species is also a potential natural vagrant to Western Europe and there have been records in areas such as Cornwall and the Isles of Scilly which some observers consider may relate to wild birds ; however, given the Wood Duck's popularity in captivity it would be extremely difficult to prove their provenance one way or another.
* Given a partial function f from the natural numbers into the natural numbers, f is a partial recursive function if and only if the graph of f, that is, the set of all pairs such that f ( x ) is defined, is recursively enumerable.
Given and question
The question concerned the educational value of pre-Christian classical thought: " Given that the body of knowledge of the pre-Christian Romans was heathen in origin, was it safe to teach it to Christian children?
* Question answering: Given a human-language question, determine its answer.
" As Shelly Kagan says, “ Given the parameters of the actual world, there is no question that …( maximally )… promoting the good would require a life of hardship, self-denial, and austerity … a life spent promoting the good would be a severe one indeed .”
Given the abundance of such optimization problems in everyday life, a positive answer to the " P vs. NP " question would likely have profound practical and philosophical consequences.
Given the structure of the experiment, it may or may not be possible to actually perform it, and, in the case that it is possible for it to be performed, there need be no intention of any kind to actually perform the experiment in question.
Given these objections to creole as a concept, articles such as Against Creole Exceptionalism and Deconstructing Creole have arisen which question the idea that creoles are exceptional in any meaningful way.
Given that question time is the only time of day when all members of Parliament are in their respective chambers, the appearance of question time can be rowdy and boisterous compared to the normally sedate activity during the rest of the day.
Given the composition of the current 41st Canadian Parliament, once the Official Opposition, the New Democratic Party, is finished, the next question comes from the only other officially-recognized opposition party, the Liberal Party.
Given the value of p, and no other information relevant to the question of whether the sun will rise tomorrow, the probability that the sun will rise tomorrow is p. But we are not " given the value of p ".
Given a subset A of G, the measure can be thought of as answering the question: what is the probability that a random element of G is in A?
Given the example above, the two galaxies in question cannot have shared any sort of information ; they are not in " causal contact ".
Given that the ESCP is a regulation and not a directive, it is arguable whether it has left too many aspects to the discretion of member states, which could call into question the legal certainty expected from a European regulation.
The optimization attempts to answer the question: " Given our operating constraints, what is the best mix of products and / or services for us to produce and sell in the period, and at what prices, to generate the highest expected revenue?
For example, more people will likely answer " yes " to the question " Given the increasing burden of taxes on middle-class families, do you support cuts in income tax?
Given a rapidly changing technological and market environment, many in the public policy area question the government's ability to make and maintain meaningful regulation that doesn't cause more harm than good.
Given the interconnection of s and k in steady state, noted above, the question can be phrased: " How much capital per worker ( k ) is needed to achieve the maximum level of consumption per worker in the steady state?
Given this, the question of whether the canola in his fields in 1997 arrived there accidentally was ruled to be irrelevant.
Given the secrecy surrounding their situation, the question is not easy to answer: probably the conversos themselves were divided, and could be ranged at different points between the possible positions.
Given the quality of his performance, and the uncertainty over Brady's recovery, NFL analysts and reporters raised the question of whether the Patriots should, or would, franchise Cassel, less than three months after some of those same reporters predicted Cassel would be cut from the team.
Given that the function is analytic within each of these quarters, a nonzero winding number N ( always an integer ) identifies N zeros of the function inside the quarter in question, each zero counted as many times as its multiplicity.
2.424 seconds.