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Correspondence graphs #1246

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merged 11 commits into from Apr 9, 2022
Merged

Correspondence graphs #1246

merged 11 commits into from Apr 9, 2022

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maggesi
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@maggesi maggesi commented Jun 28, 2019

Alternative representation of graphs as a "correspondence" relation (here called CGraphs for short)
E -> V * V
and its categorical structure.

What is missing:

  • proof that the category of CGraphs is univalent;
  • proof that CGraphs are weakly equivalent to Graphs (the proof that pre-CGraphs and pre-Graphs are weakly equivalent is done).

: arc G → node G
:= pr222 G.

Definition has_nodeset (G : precgraph) : UU
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It would be nice to put these in hProp

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However, it becomes less easy to use it I think.

: cgraph_mor G H
:= p₀,, p₁,, h.

Definition onnode {G H : precgraph}
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Suggested change
Definition onnode {G H : precgraph}
Definition on_node {G H : precgraph}

: cgraph_mor G H → node G → node H
:= pr1.

Definition onarc {G H : precgraph}
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Suggested change
Definition onarc {G H : precgraph}
Definition on_arc {G H : precgraph}

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These will be presumably used quite often. I think it is better to squeeze as much as possible.

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@langston-barrett langston-barrett left a comment

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I think less abbreviation and more underscores would improve readability, but I like the content.

maggesi and others added 9 commits July 25, 2019 23:49
Co-Authored-By: Langston Barrett <langston.barrett@gmail.com>
Co-Authored-By: Langston Barrett <langston.barrett@gmail.com>
Co-Authored-By: Langston Barrett <langston.barrett@gmail.com>
Co-Authored-By: Langston Barrett <langston.barrett@gmail.com>
@benediktahrens
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@maggesi : apologies for the slow handling of this PR!

@benediktahrens benediktahrens merged commit 05072cc into UniMath:master Apr 9, 2022
Skantz pushed a commit to Skantz/UniMath that referenced this pull request Nov 12, 2022
Skantz pushed a commit to Skantz/UniMath that referenced this pull request Nov 12, 2022
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4 participants