If C is a complete category, then, by the above existence theorem for limits, a functor G: C → D is continuous if and only if it preserves ( small ) products and equalizers.

The urgency ( to put it that way ) of the problem for the geometers accounts for the title of the 1959 Grothendieck seminar TDTE on theorems of descent and techniques of existence ( see FGA ) connecting the descent question with the representable functor question in algebraic geometry in general, and the moduli problem in particular.

The definition is usually given in this way because it reveals the existence of a canonical functor

Together with the existence property it translates to the assertion that is an indecomposable projective object – the functor it represents ( i. e., the global-section functor ) preserves epis and coproducts ( Freyd and Scedrov 1990 ).

Namely, we can demand the existence of a tensor product that is left adjoint to the internal Hom functor.

) In a characteristic turn, Grothendieck reformulated general coherent duality as the existence of a right adjoint functor f < sup > !</ sup >, called twisted or exceptional inverse image functor, to a higher direct image with compact support functor Rf < sub >!</ sub >.

Thus, it is no mystical intuition, but an analyzable conception to say that man and his tradition can `` fall out of existence ''.

The existence of a public school vocational training program in trade and industry provides a base from which such needs can be filled.

Thus, besides the training provided to youth in school, the existence of the school program can have supplementary benefits to industry which make it an asset to industrial development efforts.

" The problem then becomes that of constructing a well-ordering, which turns out to require the axiom of choice for its existence ; every set can be well-ordered if and only if the axiom of choice holds.

Agnosticism is the view that the truth values of certain claims — especially claims about the existence or non-existence of any deity, but also other religious and metaphysical claims — are unknown and ( so far as can be judged ) unknowable.

Characteristic of the Sahara is the date palm, which flourishes where other vegetation can scarcely maintain existence, while in the semidesert regions the acacia, from which gum arabic is obtained, is abundant.

Similarly, intuitionists object to the existence property for classical logic, where one can prove, without being able to produce any term of which holds.

The normal order of administration is: first Penance ( if the dying person is physically unable to confess, absolution, conditional on the existence of contrition, is given ); next, Anointing ; finally, Viaticum ( if the person can receive it ).

Pointing out that predicables are predicated univocally of substances ; that is, they refer to " the same thing " found in each instance, St. Thomas argued that whatever can be said about being is not univocal, because all beings are unique, each actuated by a unique existence.

As far as we can discern, the sole purpose of human existence is to kindle a light of meaning in the darkness of mere being.

Checking the existence of such a replacement can be done in linear time ; therefore, the satisfiability of such formulae is in P as it can be solved by first performing this replacement and then checking the satisfiability of the resulting Horn formula.

Abelard in his Dialectica made an argument against the idea that the copula can express existence based on a reductio ad absurdum.

Philosophers who consider subjective experience the essence of consciousness also generally believe, as a correlate, that the existence and nature of animal consciousness can never rigorously be known.

If their existence past the K – T boundary can be confirmed, these hadrosaurids would be considered a Dead Clade Walking.

As well, even though in many cases the popular change from one to the next can be swift and sudden, the beginning and end of movements are somewhat subjective, as the movements did not spring fresh into existence out of the blue and did not come to an abrupt end and lose total support, as would be suggested by a date range.

The existence of the five elements can also be found in India, predating their use in Greece.

" That is, whatever the force of the cogito, Descartes draws too much from it ; the existence of a thinking thing, the reference of the " I ," is more than the cogito can justify.

Sancho tries to restore his faith, but Alonso Quixano, for that is his true name, can only renounce his previous existence and apologize for the harm he has caused.

Some constructions of smooth manifold theory, such as the existence of tangent bundles, can be done in the topological setting with much more work, and others cannot.

Divination can be seen as a systematic method with which to organize what appear to be disjointed, random facets of existence such that they provide insight into a problem at hand.

Only when the core of existence stands revealed as a social process can existence be seen as the product, albeit the hitherto unconscious product, of human activity ".

Thus Ockham argued that " Socrates has wisdom ", which apparently asserts the existence of a reference for " wisdom ", can be rewritten as " Socrates is wise ", which contains only the referring phrase " Socrates ".

However, this argument may be inverted by realists in arguing that since the sentence " Socrates is wise " can be rewritten as " Socrates has wisdom ", this proves the existence of a hidden referent for " wise ".

For less than a dozen miles from the unplowed land of the dead man lived another settler who had ignored the warnings that his existence might be foreclosed on -- a blatant and defiant rustler named Fred Powell.

When Heidegger and Sartre speak of a contrast between being and existence, they may be right, I don't know, but their language is too philosophical for me.

Whitehead contends that the human way of understanding existence as a unity of interlocking and interdependent processes which constitute each other and which cause each other to be and not to be is possible only because the basic form of such an understanding, for all its vagueness and tendency to mistake the detail, is initially given in the way man feels the world.

Such characters, with their low existence and often low morality, produce humorous effects in his novels and tales, as they did in the writing of Longstreet and Hooper and Harris, but it need not be added that he gives them far subtler and more intricate functions than they had in the earlier writers ; ;

but the basic puzzles of existence would still be puzzling, and we should still have to work out the sort of problems we plan to discuss in this article.

When combined with the metaphysical notion that pure forms of this universe are best appreciated when least embodied in a material substratum, it becomes clear that while earth will be dross on a scale of material-formal ratios, celestial bodies will be of a subtle, quickened, ethereal existence, in whose embodiment pure form will be the dominant component and matter will be absent or remain subsidiary.

While I fully agree with Sir Anthony's contention, I think that we must carry the analysis farther, bearing in mind that while common peril may be the measure of our need, the existence or absence of a positive sense of community must be the measure of our capacity.

When the fate of the individual is visited on the group, then ( the warm sweet butter dripped from her raised trembling fork and she pushed her head forward belligerently ), ah, then the true bitterness of existence could be tasted.

in the case of a partnership or corporation, the existence of which has been terminated and on behalf of which an award is made, payment shall be made, except as provided in paragraphs ( 3 ) and ( 4 ), to the person or persons found by the Comptroller General of the United States to be entitled thereto ; ;

They may be unaware of the existence of lower-class values and consequently fail to take them into account.

When we say that a mythological mode of thought must be completely abandoned, we mean it must be abandoned as the sole or proper means for presenting the Christian understanding of existence.

But one does not have to affirm the existence of an evil order irredeemable in that sense, or a static order in which no changes will take place in time, to be able truthfully to affirm the following fact: there has never been justitia imprinted in social institutions and social relationships except in the context of some pax-ordo preserved by clothed or naked force.

We should not allow the image of an immanent end brought about indirectly by our own action in the continuing human struggle for a just endurable order of existence to blind us to the fact that in some measure accelerating the end of our lease may be one consequence among others of many other of mankind's thrusts toward we know not what future.

However, the Greek tradition is referring to the existence of vapours and chewing of laurel-leaves, which seem to be confirmed by recent studies.

In fact, he said explicitly that there were no structural problems with the verb " to be " when used as an auxiliary verb or when used to state existence or location.

It is also consistent with ZF + DC that every set of reals is Lebesgue measurable ; however, this consistency result, due to Robert M. Solovay, cannot be proved in ZFC itself, but requires a mild large cardinal assumption ( the existence of an inaccessible cardinal ).