## Morphism

In mathematics, a **morphism** is an abstraction derived from **structure-preserving mappings** between two mathematical structures. The notion of morphism recurs in much of contemporary mathematics. In set theory, morphisms are functions; in linear algebra, linear transformations; in group theory, group homomorphisms; in topology, continuous functions, and so on.

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### Some articles on morphism:

Early Work On Cotangent Complexes

... gave a definition when f is a smoothable

... gave a definition when f is a smoothable

**morphism**, meaning there is a scheme V and**morphisms**i X → V and h V → Y such that f = hi, i is a closed ... For example, all projective**morphisms**are smoothable, since V can be taken to be a projective bundle over Y.) In this case, he defines the cotangent complex of f as an object in the derived ... definition is independent of the choice of V and that for a smoothable complete intersection**morphism**, this complex is perfect ...**Morphism**- Examples

... concrete categories studied in universal algebra (groups, rings, modules, etc.),

**morphisms**are usually homomorphisms ... In the category of topological spaces,

**morphisms**are continuous functions and isomorphisms are called homeomorphisms ... In the category of smooth manifolds,

**morphisms**are smooth functions and isomorphisms are called diffeomorphisms ...

List Of Zero Terms - Zero

... A zero

**Morphism**s... A zero

**morphism**in a category is a generalised absorbing element under function composition any**morphism**composed with a zero**morphism**gives a zero ... Specifically, if 0XY X → Y is the zero**morphism**among**morphisms**from X to Y, and f A → X and g Y → B are arbitrary**morphisms**, then g ∘ 0XY = 0XB and 0XY ∘ f = 0AY ... zero object 0, then there are canonical**morphisms**X → 0 and 0 → Y, and composing them gives a zero**morphism**0XY X → Y ...Properties of The Cotangent Complex - Vanishing Properties

... If f is an étale

... If f is an étale

**morphism**, then LB/A = 0 ... If f is a smooth**morphism**, then LB/A is quasi-isomorphic to ΩB/A ... If f is a local complete intersection**morphism**, then LB/A has projective dimension at most one ...Finite

... In algebraic geometry, a branch of mathematics, a

**Morphism**... In algebraic geometry, a branch of mathematics, a

**morphism**of schemes is a finite**morphism**if has an open cover by affine schemes such that for each , is an open affine subscheme, and the restriction of ...