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:

Virtual appliance

A virtual appliance is a pre-configured virtual machine image, ready to run on a hypervisor; virtual appliances are a subset of the broader class of software appliances. Installation of a software appliance on a virtual machine and packaging that into an image creates a virtual appliance. Like software appliances, virtual appliances are intended to eliminate the installation, configuration and maintenance costs associated with running complex stacks of software.

A virtual appliance is not a complete virtual machine platform, but rather a software image containing a software stack designed to run on a virtual machine platform which may be a Type 1 or Type 2 hypervisor. Like a physical computer, a hypervisor is merely a platform for running an operating system environment and does not provide application software itself.

Many virtual appliances provide a Web page user interface to permit their configuration. A virtual appliance is usually built to host a single application; it therefore represents a new way to deploy applications on a network. Virtual machining is also a Virtual appliance in order to produce actual parts in virtual environments.

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

Formal language

In mathematics, computer science, and linguistics, a formal language is a set of strings of symbols that may be constrained by rules that are specific to it.

The alphabet of a formal language is the set of symbols, letters, or tokens from which the strings of the language may be formed; frequently it is required to be finite. The strings formed from this alphabet are called words, and the words that belong to a particular formal language are sometimes called well-formed words or well-formed formulas. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar, also called its formation rule.

The field of formal language theory studies primarily the purely syntactical aspects of such languages—that is, their internal structural patterns. Formal language theory sprang out of linguistics, as a way of understanding the syntactic regularities of natural languages. In computer science, formal languages are used among others as the basis for defining the grammar of programming languages and formalized versions of subsets of natural languages in which the words of the language represent concepts that are associated with particular meanings or semantics. In computational complexity theory, decision problems are typically defined as formal languages, and complexity classes are defined as the sets of the formal languages that can be parsed by machines with limited computational power. In logic and the foundations of mathematics, formal languages are used to represent the syntax of axiomatic systems, and mathematical formalism is the philosophy that all of mathematics can be reduced to the syntactic manipulation of formal languages in this way.

Language (journal)

Language is a peer-reviewed quarterly academic journal published by the Linguistic Society of America since 1925. It covers all aspects of linguistics, focusing on the area of theoretical linguistics. Its current editor-in-chief is Gregory Carlson (University of Rochester).

Under the editorship of Yale linguist Bernard Bloch, Language was the vehicle for publication of many of the important articles of American structural linguistics during the second quarter of the 20th century, and was the journal in which many of the most important subsequent developments in linguistics played themselves out.

One of the most famous articles to appear in Language was the scathing 1959 review by the young Noam Chomsky of the book Verbal Behavior by the behaviorist cognitive psychologist B. F. Skinner. This article argued that Behaviorist psychology, then a dominant paradigm in linguistics (as in psychology at large), had no hope of explaining complex phenomena like language. It followed by two years another book review that is almost as famous—the glowingly positive assessment of Chomsky's own 1957 book Syntactic Structures by Robert B. Lees that put Chomsky and his generative grammar on the intellectual map as the successor to American structuralism.

Language Spoken at Home in the United States of America

Language Spoken at Home is a data set published by the United States Census Bureau on languages in the United States. In 2000 and 1990, it was a part of Summary File 3, collected from the long-form questionnaire which was distributed to 1 out of 6 households. The data set is put to use by governments and other organizations in determining which languages to use in a specific geographic area; for instance in voting machines, literature for voters, and material for public libraries. This question was first asked in 1980; It replaced a question about one's mother language.

The published data is for 30 languages, chosen for their nationwide distribution, and 10 language groupings (see list below). Data from households which report languages other than the 30 are reported under the language groupings. Thus, languages which are widespread in certain areas of the country but not nationally get put together, even in block level data. Lithuanian, and Welsh are simply "Other Indo-European languages," Yoruba and Swahili are simply "African languages," and Indonesian and Syriac are simply "Other Asian languages." Several locally very well represented languages, such as Punjabi and Pennsylvania German, are collated into smaller groupings. Native North American languages besides Navajo are also collated, though they are reported on several geographic levels in another data set.