Abelian Category
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Abelian Category
In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no general consensus abo ..., an abelian category is a category Category, plural categories, may refer to: Philosophy and general uses *Categorization, categories in cognitive science, information science and generally * Category of being * ''Categories'' (Aristotle) *Category (Kant) *Categories (Peirce) *C ... in which morphism In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It h ...s and objects can be added and in which kernel Kernel may refer to: Computing * Kernel (operating system) The kernel is a computer program at the core of a co ...
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Mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no general consensus about its exact scope or . Most of mathematical activity consists of discovering and proving (by pure reasoning) properties of . These objects are either s from nature (such as s or "a "), or (in modern mathematics) abstract entities that are defined by their basic properties, called s. A consists of a succession of applications of some to already known results, including previously proved s, axioms and (in case of abstraction from nature) some basic properties that are considered as true starting points of the theory under consideration. The result of a proof is called a ''theorem''. Contrary to s, the validity of a theorem (its truth) does not rely on any but on the correctness of its reasoning (though experimentation is often useful for ...
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