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#the morphisms from a natural number ''n'' to itself are the elements of the [[symmetric g #there are no morphisms from ''m'' to ''n'' if <math>m\neq n</math>. ...

For finitely presented morphisms, formal smoothness is equivalent to [[Smooth morphism|usual]] notion of smo === Smooth morphisms === ...

...a universal homeomorphism if and only if it is [[integral element#Integral morphisms|integral]], [[radicial morphism|radicial]] and surjective.<ref>EGA IV<sub>4 [[Category:Morphisms of schemes]] ...

...web|url=http://ukcatalogue.oup.com/product/9780198503620.do|title=Harmonic Morphisms Between Riemannian Manifolds|work=Oxford University Press}}</ref> ...tinuous function called the [[dilation (metric space)|dilation]]. Harmonic morphisms are therefore solutions to [[non-linear]] [[over-determined system]]s of [[ ...

== Finite morphisms in algebraic geometry == ...eometry)|scheme]]s can be found in the article on [[Finite morphism|finite morphisms]]. ...

...a δ-functor satisfying a specific universal property related to extending morphisms beyond "degree 0". These notions were introduced by [[Alexander Grothendiec ...δ-functor''' are sometimes used to distinguish between the case where the morphisms "go down" (''homological'') and the case where they "go up" (''cohomologica ...

...definitions of an '''fpqc morphism''', both variations of faithfully flat morphisms. * The composite of fpqc morphisms is fpqc. ...

...symplectomorphisms be augmented by the inclusion of canonical relations as morphisms." The composition of canonical relations is given by a [[fiber product]]. ...

...n (computer science)|evaluation map ]] in the [[Comma category|category of morphisms]] of <math>\mathbf{C}</math>. === Set elements as morphisms from terminal objects === ...

More generally, one can also consider a morphism between [[Prestack#Morphisms|prestacks]] (a stackification would be an example). ...]], Ch, 83, [http://stacks.math.columbia.edu/download/stacks-morphisms.pdf Morphisms of algebraic stacks] ...

...ath>K</math>, and <math>\Gamma</math> and <math>\Phi</math> two classes of morphisms in <math>K</math>. The definition{{sfn|Akbarov|2016|p=52}} of a refinement ...th> in the class of morphisms <math>\Gamma</math> by means of the class of morphisms <math>\Phi</math>'', if <math>\sigma\in\Gamma</math>, and for any morphism ...

...object of objects' and 'object of morphisms'—together with a collection of morphisms in the ambient category satisfying certain identities. [[Group object]]s, a ...ath>-objects <math>C_0,C_1</math> named "object of objects" and "object of morphisms" respectively and four <math>C</math>-arrows <math>d_0,d_1:C_1\rightarrow C ...

...') and whose morphisms from (''X'',&nbsp;''f'') to (''Y'',&nbsp;''g'') are morphisms ''h'' in ''C'' from ''X'' to ''Y'' such that <math>G(h) \circ f = g \circ F ...

...a)|rng]]s (not [[ring (mathematics)|ring]]s!) together with multiplicative morphisms is pseudo-abelian. ...<math>C</math> and <math>p</math> is an idempotent of <math>X</math>. The morphisms ...

...ary of algebraic geometry|integral separated]] scheme of [[finite morphism#Morphisms of finite type|finite type]] over ''k''.<ref name=St020D>{{Citation | title ...'' and ''Z'' → ''Y'', there is a scheme ''X'' ×_''Y'' ''Z'' with morphisms to ''X'' and ''Z'', making the diagram ...

...undle''' is a [[fiber bundle]] whose typical fiber, fibers, trivialization morphisms and transition functions are affine.<ref>{{citation|last1=Kolář|first1=Ivan ...an affine bundle atlas of <math>Y\to X</math> whose local trivializations morphisms and transition functions are [[affine transformation|affine isomorphisms]]. ...

[[Category:Morphisms of schemes]] ...

...<math>K</math> formed by the [[vector space]] having the elements of (the morphisms of) <math>G</math> as [[generator (mathematics)|generator]]s and having the ...te]] number of [[object (category theory)|object]]s and a finite number of morphisms, the groupoid algebra is a [[direct sum]] of [[tensor product]]s of group a ...

Given a [[class (mathematics)|class]] ''C'' of morphisms in a [[model category]] ''M'' the left Bousfield localization is a new mode ...ets) a certain simplicial set whose set of [[path component]]s agrees with morphisms in the [[homotopy category]] of ''M'': ...

...n the composition is well-defined only up to still higher order invertible morphisms, etc. ...ea of higher category theory (at least, higher category theory when higher morphisms are invertible) is that, as opposed to the standard notion of a category, t ...