Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. Plural form of morphism.
Etymologies
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Examples

What matters is the way an object is related to the other objects of the category, that is, the morphisms going in and the morphisms going out, or, put differently, how certain structures can be mapped into a given object and how a given object can map its structure into other structures of the same kind.

: A sequence of algebraic objects and morphisms which is used to describe or analyse algebraic structure.

Build a category by taking the points in phase space as your objects and timeevolution operations as your morphisms.

A problem concerning institution morphisms is that formulas involving connectives from different logics being combined are not allowed.

Categories of logic systems having logic translations as morphisms are such that the canonical injections of the coproduct are just inclusion mappings.

As it will be shown in Section the different notions of morphisms between logics affect the strength of the logics obtained by algebraic fibring in the different categories of logic systems.

The category Vec with objects vector spaces and morphisms linear maps.

The category Top with objects topological spaces and morphisms continuous functions.

C to morphisms of D, in such a way that composition of morphisms in C is preserved, i.e.,

The categories Lat and Bool with objects lattices and Boolean algebras, respectively, and morphisms structure preserving homomorphisms, i.e., (¤, ¥, §, ¨) homomorphisms.
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