diff --git a/flake.lock b/flake.lock
index cc0a181..df5f71d 100644
--- a/flake.lock
+++ b/flake.lock
@@ -158,11 +158,12 @@
     },
     "flake-schemas": {
       "locked": {
-        "narHash": "sha256-ifw8Td8kD08J8DxFbYjeIx5naHcDLz7s2IFP3X42I/U=",
-        "rev": "c702cbb663d6d70bbb716584a2ee3aeb35017279",
-        "revCount": 21,
+        "lastModified": 1697467827,
+        "narHash": "sha256-j8SR19V1SRysyJwpOBF4TLuAvAjF5t+gMiboN4gYQDU=",
+        "rev": "764932025c817d4e500a8d2a4d8c565563923d29",
+        "revCount": 29,
         "type": "tarball",
-        "url": "https://api.flakehub.com/f/pinned/DeterminateSystems/flake-schemas/0.1.1/018a4c59-80e1-708a-bb4d-854930c20f72/source.tar.gz"
+        "url": "https://api.flakehub.com/f/pinned/DeterminateSystems/flake-schemas/0.1.2/018b3da8-4cc3-7fbb-8ff7-1588413c53e2/source.tar.gz"
       },
       "original": {
         "type": "tarball",
@@ -339,11 +340,11 @@
         "nixpkgs-regression": "nixpkgs-regression_2"
       },
       "locked": {
-        "lastModified": 1695206941,
-        "narHash": "sha256-ggISAuGpTkKp6JXt1BbcLtLDYOPECWqrVnPVgQEFHYc=",
+        "lastModified": 1696259154,
+        "narHash": "sha256-WNmifcTsN9aG1ONkv+l2BC4sHZZxtNKy0keqBHXXQ7w=",
         "owner": "NixOS",
         "repo": "nix",
-        "rev": "44fb1192185cdd03343da7faa08a1c605f773419",
+        "rev": "f5f4de6a550327b4b1a06123c2e450f1b92c73b6",
         "type": "github"
       },
       "original": {
@@ -388,11 +389,11 @@
     },
     "nixpkgs": {
       "locked": {
-        "lastModified": 1696019113,
-        "narHash": "sha256-X3+DKYWJm93DRSdC5M6K5hLqzSya9BjibtBsuARoPco=",
+        "lastModified": 1697723726,
+        "narHash": "sha256-SaTWPkI8a5xSHX/rrKzUe+/uVNy6zCGMXgoeMb7T9rg=",
         "owner": "NixOS",
         "repo": "nixpkgs",
-        "rev": "f5892ddac112a1e9b3612c39af1b72987ee5783a",
+        "rev": "7c9cc5a6e5d38010801741ac830a3f8fd667a7a0",
         "type": "github"
       },
       "original": {
diff --git a/overlays/overrides/default.nix b/overlays/overrides/default.nix
index 2434dff..0e329d7 100644
--- a/overlays/overrides/default.nix
+++ b/overlays/overrides/default.nix
@@ -13,7 +13,7 @@
 # You should have received a copy of the GNU General Public License
 # along with this program. If not, see <http://www.gnu.org/licenses/>.
 
-{ hydra, nix, ... } @ inputs:
+{ hydra, nix, ... } @ _inputs:
 final: prev:
 let
   # Avoid infinite recursion by renaming flakes
@@ -27,11 +27,26 @@ let
   hydra_final = final // (hydra'.inputs.nix.overlays.default hydra_final prev);
   # Get the relevant bits out of the provided overlays
   inherit (hydra'.overlays.default hydra_final prev) hydra perlPackages;
-  inherit (nix'.overlays.default final prev) lowdown-nix nix;
+  inherit (nix'.overlays.default final prev) lowdown-nix nix nixStable nixUnstable;
 
 in
 {
   # Expose the extracted packages into the overlay
-  inherit lowdown-nix nix perlPackages;
+  inherit lowdown-nix nix nixStable nixUnstable perlPackages;
+  nixVersions = with final; prev.nixVersions // {
+    schemas = nixSchemas;
+  };
   hydra_unstable = hydra;
+
+  # Build a nix package that has flake schema support (see nix#8892)
+  nixSchemas = nix.overrideAttrs ({ patches ? [ ], ... }: {
+    patches = patches ++ [
+      (final.fetchpatch {
+        url = "https://github.com/NixOS/nix/pull/8892.diff";
+        hash = "sha256-NfBksfuW1RUWe3O9cyqdM+A4O9ZGvEWg8rfv+24BosA=";
+        excludes = [ "doc/manual/src/SUMMARY.md.in" "flake.nix" "flake.lock" ];
+      })
+    ];
+    doCheck = false; # Schema tests still require internet connection
+  });
 }
diff --git a/schemas/apps/default.nix b/schemas/apps/default.nix
new file mode 100644
index 0000000..3ed0b78
--- /dev/null
+++ b/schemas/apps/default.nix
@@ -0,0 +1,31 @@
+# This file is part of Nix++.
+# Copyright (C) 2023 Leandro Emmanuel Reina Kiperman.
+#
+# Nix++ is free software: you can redistribute it and/or modify it under the
+# terms of the GNU General Public License as published by the Free Software
+# Foundation, either version 3 of the License, or (at your option) any later
+# version.
+#
+# Nix++ is distributed in the hope that it will be useful, but WITHOUT ANY
+# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
+# A PARTICULAR PURPOSE. See the GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program. If not, see <http://www.gnu.org/licenses/>.
+
+{ ... } @ _inputs:
+{
+  version = 1;
+  doc = ''
+    The `apps` flake output is a set of executables that can be run using `nix run`.
+  '';
+  inventory = output: {
+    children = builtins.mapAttrs
+      (system: apps: {
+        forSystems = [ system ];
+        children = builtins.mapAttrs (_: _: { what = "flake app"; }) apps;
+      })
+      output
+    ;
+  };
+}
diff --git a/schemas/default.nix b/schemas/default.nix
index 65309a1..be5763f 100644
--- a/schemas/default.nix
+++ b/schemas/default.nix
@@ -17,13 +17,13 @@
 (self.lib.import.asSchemas' {
   path = ./.;
   apply = _: schema: schema inputs;
-  # TODO apps nixosModules packages templates
 }) // {
   inherit (flake-schemas.schemas)
     devShells
     checks
-    hydraJobs
+    # hydraJobs # Reimplemented to avoid nesting into cross compiled jobs
     nixosConfigurations
+    nixosModules
     overlays
     # packages # We have a superset that also allows for cross-compilation
     schemas
diff --git a/schemas/hydraJobs/default.nix b/schemas/hydraJobs/default.nix
new file mode 100644
index 0000000..fc8be79
--- /dev/null
+++ b/schemas/hydraJobs/default.nix
@@ -0,0 +1,55 @@
+# This file is part of Nix++.
+# Copyright (C) 2023 Leandro Emmanuel Reina Kiperman.
+#
+# Nix++ is free software: you can redistribute it and/or modify it under the
+# terms of the GNU General Public License as published by the Free Software
+# Foundation, either version 3 of the License, or (at your option) any later
+# version.
+#
+# Nix++ is distributed in the hope that it will be useful, but WITHOUT ANY
+# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
+# A PARTICULAR PURPOSE. See the GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program. If not, see <http://www.gnu.org/licenses/>.
+
+{ nixpkgs, ... } @ _inputs:
+{
+  version = 1;
+  doc = ''
+    The `hydraJobs` flake output defines derivations to be built by the Hydra
+    continuous integration system.
+  '';
+  inventory = output: {
+    children = builtins.mapAttrs
+      (_: category: {
+        children = builtins.mapAttrs
+          (name: jobset:
+            let
+              localSystem = builtins.head (nixpkgs.lib.splitString "." name);
+              crossSystem = nixpkgs.lib.removePrefix "${localSystem}." name;
+
+            in
+            {
+              forSystems = [ localSystem ];
+              children = builtins.mapAttrs
+                (_: job: {
+                  what = "Hydra CI job (${
+                    if localSystem == crossSystem then
+                      "natively compiled on ${localSystem}"
+                    else
+                      "cross compiled on ${localSystem} for ${crossSystem}"
+                  })";
+                  derivation = job;
+                })
+                jobset
+              ;
+            }
+          )
+          category
+        ;
+      })
+      output
+    ;
+  };
+}
diff --git a/schemas/lib/default.nix b/schemas/lib/default.nix
index e72d506..db80f78 100644
--- a/schemas/lib/default.nix
+++ b/schemas/lib/default.nix
@@ -29,6 +29,9 @@ let
       _apply = metadata: {
         what = "Metadata for this flake";
       } // recurse metadata [ "meta" ];
+      homepage._apply = _: {
+        what = "This flake's home page";
+      };
       license._apply = _: {
         what = "GPLv3+ license";
       };
@@ -41,6 +44,7 @@ let
       what = "Cross-compiled nixpkgs with overlays applied";
       children = builtins.mapAttrs
         (localSystem: crossPkgs: {
+          forSystems = [ localSystem ];
           children = builtins.mapAttrs
             (crossSystem: _: {
               what = "nixpkgs (${
diff --git a/schemas/packages/default.nix b/schemas/packages/default.nix
new file mode 100644
index 0000000..1e06dc4
--- /dev/null
+++ b/schemas/packages/default.nix
@@ -0,0 +1,72 @@
+# This file is part of Nix++.
+# Copyright (C) 2023 Leandro Emmanuel Reina Kiperman.
+#
+# Nix++ is free software: you can redistribute it and/or modify it under the
+# terms of the GNU General Public License as published by the Free Software
+# Foundation, either version 3 of the License, or (at your option) any later
+# version.
+#
+# Nix++ is distributed in the hope that it will be useful, but WITHOUT ANY
+# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
+# A PARTICULAR PURPOSE. See the GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program. If not, see <http://www.gnu.org/licenses/>.
+
+{ nixpkgs, self, ... } @ _inputs:
+{
+  version = 1;
+  doc = ''
+    The `packages` flake output is a collection of packages that can be installed
+    using `nix profile install`.
+  '';
+  inventory = output: {
+    children = builtins.mapAttrs
+      (localSystem: packages: {
+        forSystems = [ localSystem ];
+        children = (builtins.mapAttrs
+          (_: derivation: {
+            what = "Derivation for (natively compiled on ${localSystem})";
+            inherit derivation;
+          })
+          (nixpkgs.lib.filterAttrs
+            (name: _:
+              (builtins.all (system: name != system) self.lib.supportedSystems)
+                && (!nixpkgs.lib.hasPrefix "_" name)
+            )
+            packages
+          )
+        ) // (builtins.listToAttrs (builtins.map
+          (crossSystem: {
+            name = crossSystem;
+            value = {
+              children = builtins.mapAttrs
+                (_: derivation: {
+                  what = "Derivation (${
+                    if localSystem == crossSystem then
+                      "natively compiled on ${localSystem}"
+                    else
+                      "cross compiled on ${localSystem} for ${crossSystem}"
+                  })";
+                  inherit derivation;
+                })
+                (nixpkgs.lib.filterAttrs
+                  (name: _: !nixpkgs.lib.hasPrefix "_" name)
+                  packages.${crossSystem}.passthru
+                )
+              ;
+            };
+          })
+          (builtins.filter
+            (name:
+              builtins.any (system: name == system)
+                self.lib.supportedSystems
+            )
+            (builtins.attrNames packages)
+          )
+        ));
+      })
+      output
+    ;
+  };
+}
diff --git a/schemas/templates/default.nix b/schemas/templates/default.nix
new file mode 100644
index 0000000..c1e81e2
--- /dev/null
+++ b/schemas/templates/default.nix
@@ -0,0 +1,29 @@
+# This file is part of Nix++.
+# Copyright (C) 2023 Leandro Emmanuel Reina Kiperman.
+#
+# Nix++ is free software: you can redistribute it and/or modify it under the
+# terms of the GNU General Public License as published by the Free Software
+# Foundation, either version 3 of the License, or (at your option) any later
+# version.
+#
+# Nix++ is distributed in the hope that it will be useful, but WITHOUT ANY
+# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
+# A PARTICULAR PURPOSE. See the GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program. If not, see <http://www.gnu.org/licenses/>.
+
+{ ... } @ _inputs:
+{
+  version = 1;
+  doc = ''
+    The `templates` flake output is used to provide ways to create new flakes using
+    `nix flake init`.
+  '';
+  inventory = output: {
+    children = builtins.mapAttrs
+      (_: _: { what = "flake template"; })
+      output
+    ;
+  };
+}
diff --git a/shells/default/default.nix b/shells/default/default.nix
index 5bed508..4415288 100644
--- a/shells/default/default.nix
+++ b/shells/default/default.nix
@@ -20,7 +20,7 @@
     # Basics
     ({ lib, pkgs, ... }: {
       name = "Nix++";
-      packages = with pkgs; [ cacert coreutils nixVersions.unstable ];
+      packages = with pkgs; [ cacert coreutils nixVersions.schemas ];
       enterShell = lib.mkBefore ''
         EDITOR="''${EDITOR:-${npppkgs.vim-minimal}/bin/vim}" # Default to vim
         export EDITOR