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Stream: practice: terminology & notation

Topic: Name for this kind of graph homomorphism?

Mike Stay (Apr 04 2024 at 17:41):

Let $G[v]$ be the subgraph of the directed graph $G$ reachable from the vertex $v$. What do you call a graph homomorphism $f:G \to H$ where
$G[v_1] \cong G[v_2] \Rightarrow H[f(v_1)] \cong H[f(v_2)]$?
"Subgraph-isomorphism-preserving" is a bit of a mouthful.

Matteo Capucci (he/him) (Apr 05 2024 at 07:02):

Is this some kind of locality property?

Mike Stay (Apr 08 2024 at 15:17):

The graphs I'm interested in have structural-equivalence-classes of terms of a process calculus as vertices and context-labeled transitions as directed edges. Induced subgraph isomorphism is essentially bisimilarity. Graph homomorphisms that preserve bisimilarity are a useful notion of morphism from one language into another that is semantic rather than syntactic. Compilation is an epi, abstract interpretation is a mono.

Chris Grossack (they/them) (Apr 08 2024 at 15:41):

Is there a reason to not call it "bisimilarity-preserving"? If $v_1$ and $v_2$ are bisimilar in $G$, then $f v_1$ and $f v_2$ should be bisimilar in $H$.

Mike Stay (Apr 08 2024 at 16:39):

That's fair. I just wondered if there was a pre-existing name for it.