Definitions

from The American Heritage® Dictionary of the English Language, 5th Edition.

  • noun In mathematical category theory, a generalization or abstraction of the concept of a structure-preserving function.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

  • noun mathematics an arrow in a category.
  • noun mathematics a map which preserves structure, in a way that depends on the branch of mathematics where it arises.

Etymologies

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Examples

  • In fact, the notion of morphism in the category of logic systems being employed is the key to create or to block interactions.

    Combining Logics

  • From the categorial point of view, the process is the same as for algebraic fibring, the only difference being that the notion of morphism is stronger.

    Combining Logics

  • Hence a preordered set is a category in which there is at most one morphism between any two objects.

    Category Theory

  • On the other hand, suppose a category of logic systems in which the preservation of rules such as (*) or (**) above is required by the very notion of morphism.

    Combining Logics

  • Ellipses in phase space — curves of constant energy — then become isomorphism classes, because the oscillator motion is periodic, and for any A and B connected by a morphism, you can find another time evolution which takes B back into A.

    Arrow of Time FAQ

  • MILMAN, The Newton diagram of an analytic morphism, and applications to differentiable functions, Bull.

    RegEM « Climate Audit

  • MILMAN, The Newton diagram of an analytic morphism, and applications to differentiable functions, Bull.

    Spurious Significance #1 « Climate Audit

  • Man, according to Spinoza, believes that everything (God, nature, man himself) acts through final causes (ends, purposes) be - cause he does not know the true causes and refers all natural phenomena to himself; that is, as if nature were directed to man's benefit (anthropocentrism) by God, who is imagined to be a sort of superman (anthropo - morphism).

    Dictionary of the History of Ideas

  • We have stated above that, in a spatial setting, an impression of symmetry arises if a design is not changed by a group of automorphisms of the space, and we add to this that, as far as design is concerned, the underlying space is a setting for it, and any auto - morphism of the space is a certain change of this setting.

    SYMMETRY AND ASYMMETRY

  • Symbolism in poetry is animism, anthropo - morphism, inspired by the truth that the universe, nature and spirit must be one at their roots.

    Dictionary of the History of Ideas

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