Image (category theory)

Given a category C and a morphism in C, the image of f is a monomorphism satisfying the following universal property:

There exists a morphism such that .

For any object Z with a morphism and a monomorphism such that , there exists a unique morphism such that .

Remarks:

The image of f is often denoted by im f or Im(f).

One can show that a morphism f is epic if and only if f = im f.

Examples

In the category of sets the image of a morphism is the inclusion from the ordinary image to . In many concrete categories such as groups, abelian groups and (left- or right) modules, the image of a morphism is the image of the correspondent morphism in the category of sets.

In any normal category with a zero object and kernels and cokernels for every morphism, the image of a morphism can be expressed as follows:

Image (board game)

Image is a board game developed by 3M released in 1971. The object of the game is to put together cards that represent an image, a description of a famous person.

External links

Image (magazine)

Image (stylised as IMAGE) is an Irish lifestyle and fashion magazine launched in 1975. It has 120,000 readers a month and is 'Ireland's best-read glossy.'

References

External links

.africa

.Africa is the proposed Internet generic Top-Level Domain (gTLD) for the African and Pan African communities and users wherever they may reside. The .africa gTLD serves as a regional domain for individuals and entities based in and out of Africa.

Status

The .Africa gTLD has not yet been delegated to any organization as registry operator. The .Africa application that was submitted by DotConnectAfrica Trust is now the subject of an unresolved disagreement with ICANN (DCA Trust vs ICANN) following an Independent Review Panel (IRP) Process that was invoked by DCA Trust under ICANN’s accountability mechanism in October 2013. The IRP was administrated by the International Center for Dispute Resolution (ICDR) of the American Arbitration Association (AAA) New York, US.

DCA Trust had passed all the new gTLD applicant evaluation criteria, but before the Initial Evaluation (IE) result was issued, a Governmental Advisory Committee GAC Objection Advice that had been issued in Beijing in April 2013 was later accepted by the ICANN Board in early June 2013 which caused the ICANN Board to instruct ICANN staff that DCA Trust’s .Africa new gTLD application will not be approved. This had caused the non-completion of the evaluation of DCA Trust’s application; which then led DCA Trust to challenge the ICANN Board decision through a series of accountability mechanism.

Africa (Toto song)

"Africa" is a 1982 song by the American rock band Toto. It was included on their 1982 album Toto IV, and released as a single in late 1982. It reached number one on the US Billboard Hot 100 chart in February 1983 and number three on the UK Singles Chart the same month. The song was written by the band's keyboardist/vocalist David Paich and drummer Jeff Porcaro.

Background

The initial idea for the song came from David Paich. Jeff Porcaro explains the idea behind the song: "a boy is trying to write a song on Africa, but since he's never been there, he can only tell what he's seen on TV or remembers in the past."

David Paich said: "At the beginning of the '80s I watched a late night documentary on TV about all the terrible death and suffering of the people in Africa. It both moved and appalled me and the pictures just wouldn't leave my head. I tried to imagine how I'd feel about if I was there and what I'd do."

Musically the song took quite some time to assemble, as Paich and Porcaro explain:

Africa (Petrarch)

Africa is an epic poem in Latin hexameters by the 14th century Italian poet Petrarch (Francesco Petrarca). It tells the story of the Second Punic War, in which the Carthaginian general Hannibal invaded Italy, but Roman forces were eventually victorious after an invasion of north Africa led by Publius Cornelius Scipio Africanus, the epic poem's hero.

Background

Africa and De viris illustribus were partially inspired by Petrarch's visit to Rome in 1337. According to Bergin and Wilson (p. ix). It seems very likely that the inspirational vision of the Eternal City must have been the immediate spur to the design of the Africa and probably De viris illustribus as well. After returning from his grand tour, the first sections of Africa were written in the valley of Vaucluse. Petrarch recalls

The fact that he abandoned it early on is not entirely correct since it was far along when he received two invitations (from Rome and from Paris) in September 1340 each asking him to accept the crown as poet laureate. A preliminary form of the poem was completed in time for the laurel coronation April 8, 1341 (Easter Sunday).