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.

More precisely, there is an adjunction between F ′ F and G G ′ with unit and counit given by the compositions:

If a functor F: C → D is one half of an equivalence of categories then it is the left adjoint in an adjoint equivalence of categories, i. e. an adjunction whose unit and counit are isomorphisms.

is just the unit η of the adjunction and the multiplication transformation

Here i is the canonical inclusion of V into T ( V ) ( the unit of the adjunction ).

The unit of form is determined subjectively: `` the Heart, by the way of the Breath, to the Line ''.

For the family is the simplest example of just such a unit, composed of people, which gives us both some immunity from, and a way of dealing with, other people.

The connective system, or network, is tailored to meet the requirements of the objective, and it is therefore not surprising that a military body acting as a single coordinated unit has a different communication network than a factory, a college, or a rural village.

The unit consists of a small motor that goes on as soon as it is plugged in.

According to Friends, the unit was organized by John Snook, a former World War 2, commando who is vice president and general manager of the telephone company.

A BTU is a unit of heat, and the BTU rating of a conditioner refers to how much heat your machine can pump out of your house in an hour.

The safest procedure is to let your builder estimate the size of the unit you need, rather than trying to do this yourself.

Still another approach to the changeable letter type of sign is a modular unit introduced by Merritt Products, Azusa, Calif..

`` Only one lumber dealer in ten is equipped to handle unit loads ; ;

only one producer in a hundred is equipped to package and ship unit loads ; ;

only one builder in a thousand is equipped to receive unit loads.

If Af is the change per unit volume in Gibbs function caused by the shear field at constant P and T, and **yr is the density of the fluid, then the total potential energy of the system above the reference height is Af.

A randomization of `` ups '' and `` downs '' is more likely than ordered `` ups '' and `` downs '' in position ( 3 ) since the hydrogen atoms are well separated and so the position of one could hardly affect the position of another, and also since ordered `` up '' and `` down '' implies a larger unit cell, for which no evidence exists.

It is assumed that the flux values increase by a factor of 2.512 per magnitude, in accordance with the opinion that the total mass flux in each unit range in magnitude is constant.

The international unit is equipotent with the USP unit adopted in 1952, which was defined as the amount of activity present in 20 mg of the USP reference substance.

Consider a simple, closed, plane curve C which is a real-analytic image of the unit circle, and which is given by Af.

His view is that every religion pertains to a community, and, conversely, every community is in one aspect a religious unit.

Where boundary maintenance describes the boundaries or limits of the group, systemic linkage is defined `` as the process whereby one or more of the elements of at least two social systems is articulated in such a manner that the two systems in some ways and on some occasions may be viewed as a single unit.

Whenever a congregation really sees itself as a unit in the universal Church, in vital relation with the whole Body of Christ and participating in His mission to the world, a necessary foundation-stone of the ecumenical movement has been laid.

The first recorded proposal for a decimal-based unit of length was the universal measure unit proposed by the English philosopher John Wilkins in 1668.

The crystal in his hand represents the universal order and also suggests the basic unit of living things.

This requires that the universal formula be converted to a formula that is intended to be used only with prescribed units, meaning the numerical quantity is implicitly assumed to be multiplying a particular unit.

The magnitude of the field at every point is calculated applying the universal law, and represents the force per unit mass on any object at that point in space.

The map from unit quaternions to rotations of 3D space described in quaternions and spatial rotation is also a universal cover.

In physics, a dimensionless physical constant ( sometimes fundamental physical constant ) is a universal physical constant that is dimensionless – having no unit attached, so its numerical value is the same under all possible systems of units.

the Lie algebra equal to the unit 1 of the universal enveloping algebra.

For a compact Riemann surface S of genus greater than 1, its universal covering space is the unit disc D on which its fundamental group Γ acts by Möbius transformations.

' This 50 %- discriminated disparity can be used as a universal unit of measurement of the psychological distance of the level of a feature in an object or situation and an internal standard of comparison in memory, such as the ' template ' for a category or the ' norm ' of recognition ( Booth & Freeman, 1993 ).

The exact lineage of Vympel is not known but the unit was formed in 1981 by the KGB Gen. Drozdov within the First Chief Directorate of the KGB, as a dedicated spetsnaz unit specialised in deep penetration, sabotage, universal direct and covert action, protection of Soviet embassies and espionage cell activation in case of war.

When the initial end point is the identity quaternion, Slerp gives a segment of a one-parameter subgroup of both the Lie group of 3D rotations, SO ( 3 ), and its universal covering group of unit quaternions, S < sup > 3 </ sup >.

The second version of Montel's theorem can be deduced from the first by using the fact that there exists a holomorphic universal covering from the unit disk to the twice punctured plane.

* Another British comedy, The Last Salute, about the Automobile Association, or ' AA ', in the 1960s showed the unit supervisor as dreaming of the new post-war Great Britain and Europe as being a Worker's Paradise of sorts, with Esperanto as the universal language.

* Wah Wah Watson – guitar, Maestro universal synthesiser system / sample and hold unit, voice bag ; vocals & bass on Doin ' It

In the societal structure of the Bouzouk there was a King and a Council of Wisemen, seven mystics who had successfully maintained universal harmony by guarding the Chprotznog, a sacred containment unit used to channel and subsequently trap evil spirits.

The leading motor unit having generated the power transmits it by a continuous shaft united between the carriages by a universal joint to the driving wheels of each carriage.

The health system offers specialized services including a new cancer center and a heart center with a 20-bed cardiac universal bed unit.