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Formally, a bifunctor is a functor whose domain is a product category.

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## Some Related Sentences

Formally and is

__Formally__organized vocational programs supported by federal funds allow high school students to gain experience in

**a**field of work which

__is__likely to lead to

**a**full-time job on graduation

**.**

__Formally__

**,**the set of all context-free languages

__is__identical to the set of languages accepted by pushdown automata ( PDA ).

More rigorously

**,**the divergence of**a**vector field F at**a**point p__is__defined as the limit of the net flow of F across the smooth boundary of**a**three dimensional region V divided by the volume of V as V shrinks to p**.**__Formally__**,**__Formally__

**,**the base

__is__known as Naval Support Facility Diego Garcia ( the US activity ) or Permanent Joint Operating Base ( PJOB ) Diego Garcia ( the UK's term ).

__Formally__

**,**there

__is__

**a**clear distinction: " DFT " refers to

**a**mathematical transformation or function

**,**regardless of how it

__is__computed

**,**whereas " FFT " refers to

**a**specific family of algorithms for computing DFTs

**.**

__Formally__

**,**oxidation state

__is__the hypothetical charge that an atom would have if all bonds to atoms of different elements were 100 % ionic

**.**

__Formally__

**,**an inner

**product**space

__is__

**a**vector space V over the field together with an inner

**product**

**,**i

**.**e., with

**a**map

__Formally__

**,**if M

__is__

**a**set

**,**the identity function f on M

__is__defined to be that function with

**domain**and codomain M which satisfies

*

__Formally__**,**when working over the reals**,**as here**,**this__is__accomplished by considering the limit as ε → 0 ; but the " infinitesimal " language generalizes directly to Lie groups over general rings**.**__Formally__

**,**

**a**profinite group

__is__

**a**Hausdorff

**,**compact

**,**and totally disconnected topological group: that

__is__

**,**

**a**topological group that

__is__also

**a**Stone space

**.**

__Formally__

**,**this sharing of dynamics

__is__referred to as universality

**,**and systems with precisely the same critical exponents are said to belong to the same universality class

**.**

__Formally__

**,**

**a**frame

__is__defined to be

**a**lattice L in which finite meets distribute over arbitrary joins

**,**i

**.**e

**.**every ( even infinite ) subset

Formally and functor

Limits and colimits in

**a****category**C are defined by means of diagrams in C**.**__Formally__**,****a**diagram of type J in C**is****a**__functor__from J to C:__Formally__

**,**given two categories C and D

**,**an equivalence of categories consists of

**a**

__functor__F: C → D

**,**

**a**

__functor__G: D → C

**,**and two natural isomorphisms ε: FG → I < sub > D </ sub > and η: I < sub > C </ sub >→ GF

**.**

__Formally__

**,**an absolute coequalizer of

**a**pair in

**a**

**category**C

**is**

**a**coequalizer as defined above but with the added property that given any

__functor__F ( Q ) together with F ( q )

**is**the coequalizer of F ( f ) and F ( g ) in the

**category**D

**.**Split coequalizers are examples of absolute coequalizers

**.**

__Formally__

**,**complexification

**is**

**a**

__functor__Vect < sub > R </ sup > → Vect < sub > C </ sup >, from the

**category**of real vector spaces to the

**category**of complex vector spaces

**.**

__Formally__

**,**the right Kan extension of along consists of

**a**

__functor__and

**a**natural transformation which

**is**couniversal with respect to the specification

**,**in the sense that for any

__functor__and natural transformation

**,**

**a**unique natural transformation

**is**defined and fits into

**a**commutative diagram

Formally and whose

__Formally__

**,**the case where only

**a**subset of parameters

**is**defined

**is**still

**a**composite hypothesis ; nonetheless

**,**the term point hypothesis

**is**often applied in such cases

**,**particularly where the hypothesis test can be structured in such

**a**way that the distribution of the test statistic ( the distribution under the null hypothesis ) does not depend on the parameters

__whose__values have not been specified under the point null hypothesis

**.**

__Formally__

**,**

**a**Lie superalgebra

**is**

**a**( nonassociative ) Z < sub > 2 </ sub >- graded algebra

**,**or superalgebra

**,**over

**a**commutative ring ( typically R or C )

__whose__

**product**

**,**called the Lie superbracket or supercommutator

**,**satisfies the two conditions ( analogs of the usual Lie algebra axioms

**,**with grading ):

__Formally__

**,**the definition only requires some invertibility

**,**so we can substitute for Q any matrix M

__whose__eigenvalues do not include − 1

**.**

__Formally__

**,**the use of

**a**reduction

**is**the function that sends each natural number n to the largest natural number m

__whose__membership in the set B was queried by the reduction while determining the membership of n in A

**.**

Formally and domain

__Formally__

**,**we are given

**a**set of hypotheses and

**a**set of manifestations ; they are related by the

__domain__knowledge

**,**represented by

**a**function that takes as an argument

**a**set of hypotheses and gives as

**a**result the corresponding set of manifestations

**.**

__Formally__

**,**

**a**unique factorization

__domain__

**is**defined to be an integral

__domain__R in which every non-zero and non-unit x of R can be written as

**a**

**product**( including an empty

**product**) of irreducible elements p < sub > i </ sub > of R and

**a**unit u:

__Formally__

**,**

**a**constraint satisfaction problem

**is**defined as

**a**triple

**,**where

**is**

**a**set of variables

**,**

**is**

**a**

__domain__of values

**,**and

**is**

**a**set of constraints

**.**

__Formally__

**,**the Common Security and Defence Policy

**is**the

__domain__of the European Council

**,**which

**is**an EU institution

**,**whereby the heads of member states meet

**.**

__Formally__

**,**if f

**is**

**a**harmonic function

**,**then f cannot exhibit

**a**true local maximum within the

__domain__of definition of f

**.**In other words

**,**either f

**is**

**a**constant function

**,**or

**,**for any point inside the

__domain__of f

**,**there exist other points arbitrarily close to at which f takes larger values

**.**

Formally and product

__Formally__

**,**we start with

**a**

**category**C with finite products ( i

**.**e

**.**C has

**a**terminal object 1 and any two objects of C have

**a**

__product__).

__Formally__

**,**two variables are inversely proportional ( or varying inversely

**,**or in inverse variation

**,**or in inverse proportion or in reciprocal proportion ) if one of the variables

**is**directly proportional with the multiplicative inverse ( reciprocal ) of the other

**,**or equivalently if their

__product__

**is**

**a**constant

**.**

__Formally__

**,**the differential appearing under the integral behaves exactly as

**a**differential: thus

**,**the integration by substitution and integration by parts formulae for Stieltjes integral correspond

**,**respectively

**,**to the chain rule and

__product__rule for the differential

**.**

__Formally__

**,**f < sub > X

**,**Y </ sub >( x

**,**y )

**is**the probability density function of ( X

**,**Y ) with respect to the

__product__measure on the respective supports of X and Y

**.**

__Formally__

**,**

**a**

__product__term P in

**a**sum of products

**is**an implicant of the Boolean function F if P implies F

**.**More precisely:

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