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In mathematics, a pullback is either of two different, but related processes: precomposition and fiber-product. Its dual is a pushforward.

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rdf:type	Thing
rdfs:label	Pullback (de) 당김 (ko) Pullback (en) 拉回 (zh)
rdfs:comment	In mathematics, a pullback is either of two different, but related processes: precomposition and fiber-product. Its dual is a pushforward. (en) 拉回（pullback）是数学中一个基本概念，涉及到两个不同但关联的程序：预复合与纤维积。与之对偶的概念是前推。 (zh)
rdfs:seeAlso	Transpose of a linear map
dct:subject	Mathematical analysis
Wikipage page ID	9413508 (xsd:integer)
Wikipage revision ID	1085251666 (xsd:integer)
Link from a Wikipage to another Wikipage	Pullback (category theory) De Rham cohomology Algebraic topology Mathematics Transpose of a linear map Pullback (cohomology) Pullback (differential geometry) Pullback bundle Function (mathematics) Linear operator Function composition Function space Functional analysis Transfer operator Algebraic geometry Fiber bundle Mathematical analysis Fibred category Pushforward (disambiguation) Category theory Section (fiber bundle) Differential forms Inverse image sheaf Cartesian square Fiber product
sameAs	Pullback Pullback Pullback Pullback Pullback
dbp:wikiPageUsesTemplate	dbt:About dbt:Annotated_link dbt:Main dbt:More_citations_needed dbt:Reflist dbt:See_also
has abstract	In mathematics, a pullback is either of two different, but related processes: precomposition and fiber-product. Its dual is a pushforward. (en) 拉回（pullback）是数学中一个基本概念，涉及到两个不同但关联的程序：预复合与纤维积。与之对偶的概念是前推。 (zh)
prov:wasDerivedFrom	wikipedia-en:Pullback?oldid=1085251666&ns=0
page length (characters) of wiki page	3245 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Pullback
is Link from a Wikipage to another Wikipage of	Volume form Inclusion map Penrose transform Positive real numbers Transpose of a linear map Pullback (differential geometry) Lagrange multipliers on Banach spaces Pushforward measure Orthodox semigroup Mapping cone (topology) Measure-preserving dynamical system Local quantum field theory Log semiring Adhesive category Amalgamation property Externalization (migration) Filters in topology Glossary of Riemannian and metric geometry Glossary of differential geometry and topology Projective variety Marusan Shōten Eilenberg–Moore spectral sequence Differentiable manifold Borel set Spectral sequence Circle bundle Grothendieck topology Pull back (disambiguation) Pushforward Nash embedding theorems Castelnuovo–de Franchis theorem Seminorm Segal space Sieve (category theory) Gysin homomorphism II Corps (India) Sigma model Flat convergence Spherically symmetric spacetime Pull-back Pull back
is Wikipage redirect of	Pull-back Pull back
is foaf:primaryTopic of	wikipedia-en:Pullback

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