diff --git a/pkgs/development/coq-modules/addition-chains/default.nix b/pkgs/development/coq-modules/addition-chains/default.nix
index f2ddacf2e308..929d23c81869 100644
--- a/pkgs/development/coq-modules/addition-chains/default.nix
+++ b/pkgs/development/coq-modules/addition-chains/default.nix
@@ -6,12 +6,14 @@ mkCoqDerivation {
   pname = "addition-chains";
   repo = "hydra-battles";
 
-  release."0.4".sha256 = "sha256:1f7pc4w3kir4c9p0fjx5l77401bx12y72nmqxrqs3qqd3iynvqlp";
+  release."0.4".sha256 = "1f7pc4w3kir4c9p0fjx5l77401bx12y72nmqxrqs3qqd3iynvqlp";
+  release."0.5".sha256 = "121pcbn6v59l0c165ha9n00whbddpy11npx2y9cn7g879sfk2nqk";
   releaseRev = (v: "v${v}");
 
   inherit version;
   defaultVersion = with versions; switch coq.coq-version [
-    { case = isGe "8.11"; out = "0.4"; }
+    { case = range "8.13" "8.14"; out = "0.5"; }
+    { case = range "8.11" "8.12"; out = "0.4"; }
   ] null;
 
   propagatedBuildInputs = [ mathcomp-ssreflect mathcomp-algebra paramcoq ];
diff --git a/pkgs/development/coq-modules/gaia-hydras/default.nix b/pkgs/development/coq-modules/gaia-hydras/default.nix
new file mode 100644
index 000000000000..c20c503d73ba
--- /dev/null
+++ b/pkgs/development/coq-modules/gaia-hydras/default.nix
@@ -0,0 +1,33 @@
+{ lib, mkCoqDerivation, coq, hydra-battles, gaia, mathcomp-zify, version ? null }:
+
+with lib; mkCoqDerivation rec {
+  pname = "gaia-hydras";
+  repo = "hydra-battles";
+
+  release."0.5".sha256 = "121pcbn6v59l0c165ha9n00whbddpy11npx2y9cn7g879sfk2nqk";
+  releaseRev = (v: "v${v}");
+
+  inherit version;
+  defaultVersion = with versions; switch coq.coq-version [
+    { case = range "8.13" "8.14"; out = "0.5"; }
+  ] null;
+
+  propagatedBuildInputs = [
+    hydra-battles
+    gaia
+    mathcomp-zify
+  ];
+
+  useDune2 = true;
+
+  meta = {
+    description = "Comparison between ordinals in Gaia and Hydra battles";
+    longDescription = ''
+      The Gaia and Hydra battles projects develop different notions of ordinals.
+      This development bridges the different notions.
+    '';
+    maintainers = with maintainers; [ Zimmi48 ];
+    license = licenses.mit;
+    platforms = platforms.unix;
+  };
+}
diff --git a/pkgs/development/coq-modules/hydra-battles/default.nix b/pkgs/development/coq-modules/hydra-battles/default.nix
index 6c3c9d88e0cb..faec5d3e330c 100644
--- a/pkgs/development/coq-modules/hydra-battles/default.nix
+++ b/pkgs/development/coq-modules/hydra-battles/default.nix
@@ -5,12 +5,14 @@ mkCoqDerivation {
   pname = "hydra-battles";
   owner = "coq-community";
 
-  release."0.4".sha256 = "sha256:1f7pc4w3kir4c9p0fjx5l77401bx12y72nmqxrqs3qqd3iynvqlp";
+  release."0.4".sha256 = "1f7pc4w3kir4c9p0fjx5l77401bx12y72nmqxrqs3qqd3iynvqlp";
+  release."0.5".sha256 = "121pcbn6v59l0c165ha9n00whbddpy11npx2y9cn7g879sfk2nqk";
   releaseRev = (v: "v${v}");
 
   inherit version;
   defaultVersion = with versions; switch coq.coq-version [
-    { case = isGe "8.11"; out = "0.4"; }
+    { case = range "8.13" "8.14"; out = "0.5"; }
+    { case = range "8.11" "8.12"; out = "0.4"; }
   ] null;
 
   propagatedBuildInputs = [ equations ];
diff --git a/pkgs/top-level/coq-packages.nix b/pkgs/top-level/coq-packages.nix
index dc657ab1df5b..b8c0926a8639 100644
--- a/pkgs/top-level/coq-packages.nix
+++ b/pkgs/top-level/coq-packages.nix
@@ -43,6 +43,7 @@ let
       flocq = callPackage ../development/coq-modules/flocq {};
       fourcolor = callPackage ../development/coq-modules/fourcolor {};
       gaia = callPackage ../development/coq-modules/gaia {};
+      gaia-hydras = callPackage ../development/coq-modules/gaia-hydras {};
       gappalib = callPackage ../development/coq-modules/gappalib {};
       goedel = callPackage ../development/coq-modules/goedel {};
       graph-theory = callPackage ../development/coq-modules/graph-theory {};