## Dashed arrow and solid arrow in category theory

In category theory,what is the difference between dashed arrow and solid arrow?I am just curious why there is not any textbook which I could find mention about it formally .heh...
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 Recognitions: Homework Help Science Advisor You mean something like this? The contexts I've seen it used in usually imply the existence and uniqueness of a certain morphism.
 yeh.That is what i mean.so solid arrow imply "forall"($$\forall$$),dashed arrow imply "exists"($$\exists$$),all right?

Recognitions:
Homework Help
 In your example,If the arrow U(g) is solid,it means $$\forall U(g)[U(g) \circ \phi = f]$$,and when the arrow U(g) is dashed,then it means $$\exists U(g)[U(g) \circ \phi = f]$$,right?