Boolean Algebra Embeddings: Defining and Understanding the Role of Monomorphisms

[quasar987]

According to my notes, the definition of an embedding from a boolean algebra B in a boolean algebra B' is an injective map f:B-->B' such that for all x,y in B, f(sup{x,y}) = sup'{f(x),f(y)} and f(Cx)=C'(f(x)), where sup is the supremum in B and sup' is the complement in B', and where C is the complement in B and C' the complement in B'.

But I read on wiki that generally, an embedding is supposed to be a monomorphism. Aren't we missing the condition f(inf{x,y}) = inf'{f(x),f(y)}?

 

[Hurkyl]

But I read on wiki that generally, an embedding is supposed to be a monomorphism. Aren't we missing the condition f(inf{x,y}) = inf'{f(x),f(y)}?

Doesn't it follow from the other ones?

 

[quasar987]

Right, because of the de Morgan laws !