If substance is the highest category and there is no substance, being, then the unity perceived in all beings by virtue of their existing must be viewed in another way.

If one statement is true in a category C then its dual will be true in the dual category C < sup > op </ sup >.

If the meet is a 5 optional meet, then the divers will perform 1 optional from each category ( Front, Back, Inward, Reverse, and Twister ) and then 1 voluntary from the category of their choice.

Likewise, a functor from G to the category of vector spaces, Vect < sub > K </ sub >, is a linear representation of G. In general, a functor G → C can be considered as an " action " of G on an object in the category C. If C is a group, then this action is a group homomorphism.

Tensor products: If C denotes the category of vector spaces over a fixed field, with linear maps as morphisms, then the tensor product defines a functor C × C → C which is covariant in both arguments.

If I is ordered ( not simply partially ordered ) and countable, and C is the category Ab of abelian groups, the Mittag-Leffler condition is a condition on the transition morphisms f < sub > ij </ sub > that ensures the exactness of.

If rotations are also considered distinct, then the pentominoes from the first category count eightfold, the ones from the next three categories ( T, U, V, W, Z ) count fourfold, I counts twice, and X counts only once.

If the appliance is one whose purpose is for light or heat ( such as an incandescent lightbulb or electric oven ) then the lighting or heating elements may be considered as a type of fire ; if so, then turning them on constitutes both " lighting a fire " ( category 37 ) and " cooking " ( a form of baking, category 11 ), and turning them off would be " extinguishing a fire " ( category 36 ).

If C is a locally small category ( i. e. the hom-sets are actual sets and not proper classes ), then each object A of C gives rise to a natural functor to Set called a hom-functor.

Any collection of objects and morphisms defines a ( possibly large ) directed graph G. If we let J be the free category generated by G, there is a universal diagram F: J → C whose image contains G. The limit ( or colimit ) of this diagram is the same as the limit ( or colimit ) of the original collection of objects and morphisms.

If J is the empty category there is only one diagram of type J: the empty one ( similar to the empty function in set theory ).

If J is a discrete category then a diagram F is essentially nothing but a family of objects of C, indexed by J.

If J is a category with two objects and two parallel morphisms from object 1 to object 2 then a diagram of type J is a pair of parallel morphisms in C. The limit L of such a diagram is called an equalizer of those morphisms.

* If J = 1, the category with a single object and morphism, then a diagram of type J is essentially just an object of C. A cone to an object X is just a morphism with codomain X.

which is natural in the variables N and F. The counit of this adjunction is simply the universal cone from lim F to F. If the index category J is connected ( and nonempty ) then the unit of the adjunction is an isomorphism so that lim is a left inverse of Δ.

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.

If the predicted half-life falls into an experimentally accessible range, such isotopes have a chance to move from the list of stable nuclides to the radioactive category, once their activity is observed.

If C is any category and I is a small category, we can form the functor category C < sup > I </ sup > having as objects all functors from I to C and as morphisms the natural transformations between those functors.

If on the other hand the taxon appears never to have been named at all, then the scientist or another qualified expert picks a type specimen and publishes a new name and an official description.

If most ( if not all ) of medieval philosophers were priests and monks, early and late Renaissance philosophers were a more heterogeneous population, including rhetors, magicians and astrologues, early empirical scientist, poets, philologists.

If a player dies while carrying a scientist, the scientist stays on the ground unconscious for a limited amount of time before teleporting back to his laboratories.

If my already well-proven invention can save innocent lives while still more research is going on, I believe it is my responsibility as a scientist to make it available.

If we consider a polarization of a shear ( transverse ) elastic wave propagating along an acoustic axis in a solid, a polarization rotation effect due to rotation of the body as a whole ( so-called, " polarization inertia effect ") can be observed too ( it was noted by Ukrainian scientist Sergii A. Sarapuloff in early 80th, as well as a corresponding modification of Green-Christoffel's tensors in Acoustics ).

If there were not this conscious entity, the scientist, then one could say merely that the fetus's characteristics are determined by heredity, rather than predetermined.

If the behavior scientist truly has demonstrated control of the behavior with the intervention, the behavior of interest should change with intervention changes.

If the circumstances are faced frankly it is not reasonable to expect this to be true.

If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.

If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.

If they avoid the use of the pungent, outlawed four-letter word it is because it is taboo ; ;

If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.

If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.

If it is an honest feeling, then why should she not yield to it??

If he thus achieves a lyrical, dreamlike, drugged intensity, he pays the price for his indulgence by producing work -- Allen Ginsberg's `` Howl '' is a striking example of this tendency -- that is disoriented, Dionysian but without depth and without Apollonian control.

If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.

If he is good, he may not be legal ; ;

If the man on the sidewalk is surprised at this question, it has served as an exclamation.

If the existent form is to be retained new factors that reinforce it must be introduced into the situation.

If we remove ourselves for a moment from our time and our infatuation with mental disease, isn't there something absurd about a hero in a novel who is defeated by his infantile neurosis??

If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.

If he is a traditionalist, he is an eclectic traditionalist.

If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.

If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.