Examples of homomorphism

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The fact that f is an algebra homomorphism is given by checking the multiplication and the unit is preserved.
Both and are complete lattice homomorphisms, and thus left adjoints.
Then f and g are full homomorphisms, but g f is not.
Homomorphism is a special case of the notion of 2-functor.
Also, between any two models, the model homomorphisms are the same as the structure homomorphisms.
An inclusion of compositive graphs is a functor such that its underlying graph homomorphism is an inclusion.
Theorem 5.3.4 (homomorphisms preserve the semantics of categorical transducers).
Our contribution is a mechanizable method to extract the homomorphism representation from a pair of sequential representations.
Then we formalize the definition of the desired homomorphism and show it has the desired properties.
The combinatorial objects, markings of generalized quadratic-like maps, are based on return-type homomorphisms.
We believe we have shown that the problem of extracting a homomorphism is nontrivial.
However, there are also many useful list functions that are not list homomorphisms.
It would be interesting to investigate whether this correspondence between open morphisms and coalgebra homomorphisms holds also for different notions of path objects and endofunctors.
It is routine to check that these constructions are mutually inverse and that strict maps are in one-to-one correspondence with algebra homomorphisms.
To show this, we need to show first that sep can be computed from the contours, and second that computing the contours is a homomorphism.

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