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commutative square diagram
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(Definition)
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Remark 0.1 One can intuitively understand commutativity as the equivalence of the two morphism paths involved, or as an internal, mirror-like symmetry property of the square diagram with respect to the top-right to bottom-left diagonal. The diagonal morphism,
 (not shown) is thus equal to both  and  . The concept of commutative diagram can be thus generalized for any polyhedron with “diagonal mirror symmetry” of morphisms oriented in the same direction of the type described for the square diagram shown above.
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"commutative square diagram" is owned by bci1.
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(view preamble)
See Also: category
| Also defines: |
diagram, square diagram, commutativity, commutative diagram |
| Keywords: |
Abelian category, morphisms, homeomorphisms, category, homomorphisms |
Cross-references: type, concept, functions, category, abelian category, square
There are 38 references to this object.
This is version 6 of commutative square diagram, born on 2009-02-13, modified 2009-05-29.
Object id is 516, canonical name is CommutativeSquareDiagram.
Accessed 733 times total.
Classification:
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Pending Errata and Addenda
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![$\displaystyle \begin{xy} *!C\xybox{ \xymatrix{ {A}\ar[r]^{f}\ar[d]_{k}&{B}\ar[d]^{g}\ {C}\ar[r]_{h}&{D} } } \end{xy}$](http://images.planetphysics.org/cache/objects/516/l2h/img2.png "$\displaystyle \begin{xy} *!C\xybox{ \xymatrix{ {A}\ar[r]^{f}\ar[d]_{k}&{B}\ar[d]^{g}\ {C}\ar[r]_{h}&{D} } } \end{xy}$")
