Let F: J → C be a diagram of type J in a category C. A cone to F is an object N of C together with a family ψ < sub > X </ sub >: N → F ( X ) of morphisms indexed by the objects of J, such that for every morphism f: X → Y in J, we have F ( f ) o ψ < sub > X </ sub >

Let J be a directed poset ( considered as a small category by adding arrows i → j if and only if i ≤ j ) and let F: J < sup > op </ sup > → C be a diagram.

Let C be a category and let J be a small index category.

Let I be a finite category and J be a small filtered category.

Let F: J → C be a diagram.

J. Todd Moye, author of Let the People Decide: Black Freedom and White Resistance Movements in Sunflower County, Mississippi, 1945-1986, said " Sunflower County has always been overwhelmingly rural " and that, at the end of the 20th century, the county had four " main towns of any size.

Todd J. Moye, author of Let the People Decide: Black Freedom and White Resistance Movements in Sunflower County, Mississippi, 1945-1986, said that the white residents of Drew " traditionally been regarded as the most recalcitrant in the count on racial matters.

* " Don't Let Your Love Go Wrong " w. George Whiting & Nat Schwartz m. J. C. Johnson

* " Let The Rest Of The World Go By " w. J. Keirn Brennan m. Ernest R. Ball

* " Please Go ' Way And Let Me Sleep " w. Cecil Mack m. J. Tim Brymn

Let me borrow that ," referring to the microphone tattoo on LL Cool J's arm which LL Cool J accused Canibus of insulting him, went hard on him, and when the final cut of the song came out it featured LL Cool J's verse after Canibus, mocking an unspecified person believed to be Canibus.

Let J be the symplectic mapping

Let E and F be two vector bundles over a differentiable manifold M. An R-linear mapping of sections is said to be a kth-order linear differential operator if it factors through the jet bundle J < sup > k </ sup >( E ).

One category on the Revlon Category Board was " Jazz ", and within months of the premiere Columbia Records issued a 1955 album of various jazz artists under the tie-in title $ 64, 000 Jazz ( CL 777, also EP B-777 ), with the following tracks: " The Shrike " ( Pete Rugolo ), " Perdido " ( J. J. Johnson, Kai Winding ), " Laura " ( Erroll Garner ), " Honeysuckle Rose " ( Benny Goodman ), " Tawny " ( Woody Herman ), " One O ' Clock Jump " ( Harry James ), " How Hi the Fi " ( Buck Clayton ), " I'm Comin ', Virginia " ( Eddie Condon ), " A Fine Romance " ( Dave Brubeck, Paul Desmond ), " I Let A Song Go Out Of My Heart " ( Duke Ellington ) and " Ain't Misbehavin '" ( Louis Armstrong ).

In addition to rap, legendary smooth jazz musician Grover Washington, Jr., a fan of the 76ers, created the song " Let It Flow ( For Dr. J )", from the album Winelight, in honor of Erving.

Among these were " Let It All Hang Out " ( a cover of the 1967 track by The Hombres ), " It Only Takes A Minute " ( a cover of Tavares ' track ) as One Hundred Ton And A Feather, " Sugar, Sugar " as Sakkarin, " Loop di Love " as Shag, " Hooked on a Feeling " ( a cover of the track by B J Thomas ), " Lazybones ", " It's The Same Old Song " ( originally by Four Tops ) as The Weathermen and " The Sun Has Got His Hat On " as Nemo.

Let us first calculate exp ( J ).

Let A be a unital commutative Banach algebra over C. Since A is then a commutative ring with unit, every non-invertible element of A belongs to some maximal ideal of A.

Let M be a smooth manifold and let x be a point in M. Let I < sub > x </ sub > be the ideal of all functions in C < sup >∞</ sup >( M ) vanishing at x, and let I < sub > x </ sub >< sup > 2 </ sup > be the set of functions of the form, where f < sub > i </ sub >, g < sub > i </ sub > ∈ I < sub > x </ sub >.

Let M be a smooth manifold and let f ∈ C < sup >∞</ sup >( M ) be a smooth function.

Let C and D be categories.

Let C and D be categories.

Let a trapezoid have vertices A, B, C, and D in sequence and have parallel sides AB and CD.

Let ( X < sub > i </ sub >, f < sub > ij </ sub >) be an inverse system of objects and morphisms in a category C ( same definition as above ).

Let H be a Hilbert space, and let H * denote its dual space, consisting of all continuous linear functionals from H into the field R or C. If x is an element of H, then the function φ < sub > x </ sub >, defined by

If V is a real vector space, then we replace V by its complexification V ⊗< sub > R </ sub > C and let g denote the induced bilinear form on V ⊗< sub > R </ sub > C. Let W be a maximal isotropic subspace, i. e. a maximal subspace of V such that g |< sub > W </ sub > = 0.

Let ρ be the initial topology on X induced by C < sub > τ </ sub >( X ) or, equivalently, the topology generated by the basis of cozero sets in ( X, τ ).

Let C be the category of vector spaces K-Vect over a field K and let D be the category of algebras K-Alg over K ( assumed to be unital and associative ).

Let U be a functor from D to C, and let X be an object of C. Then the following statements are equivalent:

Let F be an arbitrary functor from C to Set.

Let A, B, C and D be the hexes that make up a rhombus, with A and C being the non-touching pair.

Let F be a diagram that picks out three objects X, Y, and Z in C, where the only non-identity morphisms are f: X → Z and g: Y → Z.

Let the open enemy to it be regarded as a Pandora with her box opened ; ;

Let every policeman and park guard keep his eye on John and Jane Doe, lest one piece of bread be placed undetected and one bird survive.

`` Let him be now ''!!

Let us assume that it would be possible for an enemy to create an aerosol of the causative agent of epidemic typhus ( Rickettsia prowazwki ) over City A and that a large number of cases of typhus fever resulted therefrom.

Let T be a linear operator on the finite-dimensional vector space V over the field F.

Let p be the minimal polynomial for T, Af, where the Af, are distinct irreducible monic polynomials over F and the Af are positive integers.

Let Af be the null space of Af.

Let N be a linear operator on the vector space V.

Let T be a linear operator on the finite-dimensional vector space V over the field F.

Let V be a finite-dimensional vector space over an algebraically closed field F, e.g., the field of complex numbers.

Let N be a positive integer and let V be the space of all N times continuously differentiable functions F on the real line which satisfy the differential equation Af where Af are some fixed constants.

Let Q be a nonsingular quadric surface bearing reguli Af and Af, and let **zg be a Af curve of order K on Q.

Let us take a set of circumstances in which I happen to be interested on the legislative side and in which I think every one of us might naturally make such a statement.

Let the state of the stream leaving stage R be denoted by a vector Af and the operating variables of stage R by Af.

Let this be denoted by Af.

Let it be granted then that the theological differences in this area between Protestants and Roman Catholics appear to be irreconcilable.

Let not your heart be troubled, neither let it be afraid ''.

The same God who called this world into being when He said: `` Let there be light ''!!

For those who put their trust in Him He still says every day again: `` Let there be light ''!!

Let us therefore put first things first, and make sure of preserving the human race at whatever the temporary price may be ''.

Let her out, let her out -- that would be the solution, wouldn't it??