Descent (category theory)
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High Quality Content by WIKIPEDIA articles! In mathematics, the idea of descent has come to stand for a very general idea, extending the intuitive idea of 'gluing' in topology. Since the topologists' glue is actually the use of equivalence relations on topological spaces, the theory starts with some ideas on identification. A sophisticated theory resulted. It was a tribute to the efforts to use category theory to get around the alleged 'brutality' of imposing equivalence relations within geometric categories. One outcome was the eventual definition adopted in topos theory of geometric morphism, to get the correct notion of surjectivity.…mehr

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High Quality Content by WIKIPEDIA articles! In mathematics, the idea of descent has come to stand for a very general idea, extending the intuitive idea of 'gluing' in topology. Since the topologists' glue is actually the use of equivalence relations on topological spaces, the theory starts with some ideas on identification. A sophisticated theory resulted. It was a tribute to the efforts to use category theory to get around the alleged 'brutality' of imposing equivalence relations within geometric categories. One outcome was the eventual definition adopted in topos theory of geometric morphism, to get the correct notion of surjectivity.