What are morphisms?

Some articles on morphisms, morphism:

Category Of Rings - Properties - Morphisms
... studied in mathematics, there do not always exist morphisms between pairs of objects in Ring ... For example, there are no morphisms from the trivial ring 0 to any nontrivial ring ... A necessary condition for there to be morphisms from R to S is that the characteristic of S divide that of R ...
List Of Zero Terms - Zero Morphisms
... A zero morphism in a category is a generalised absorbing element under function composition any morphism composed with a zero morphism gives a zero morphism ... Specifically, if 0XY X → Y is the zero morphism among morphisms from X to Y, and f A → X and g Y → B are arbitrary morphisms, then g ∘ 0XY = 0XB and 0XY ∘ f = 0AY ... If a category has a zero object 0, then there are canonical morphisms X → 0 and 0 → Y, and composing them gives a zero morphism 0XY X → Y ...
Nisnevich Topology - Definition
... A morphism of schemes f Y → X is called a Nisnevich morphism if it is an étale morphism such that for every (possibly non-closed) point x ∈ X, there exists a point y ∈ Y such that the induced map ... A family of morphisms {uα Xα → X} is a Nisnevich cover if each morphism in the family is étale and for every (possibly non-closed) point x ∈ X, there exists α and a point y ∈ Xα s.t ... If the family is finite, this is equivalent to the morphism from to X being a Nisnevich morphism ...
Mathematical Object - Category Theory
... sets as objects and the operations thereon as morphisms between those objects ... objects reduce to mere vertices of a graph whose edges as the morphisms abstract the ways in which those objects can transform and whose structure is encoded in the ...
Factorization System
... A factorization system (E, M) for a category C consists of two classes of morphisms E and M of C such that E and M both contain all isomorphisms of C and are closed under composition ... Every morphism f of C can be factored as for some morphisms and ... The factorization is functorial if and are two morphisms such that for some morphisms and, then there exists a unique morphism making the following diagram ...