diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index a35d5fe..681a3d7 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -14,12 +14,12 @@
             "state": {
               "type": "markdown",
               "state": {
-                "file": "Concurrent Systems/notes/9 - Universal Object.md",
+                "file": "Concurrent Systems/notes/9 - Consensus.md",
                 "mode": "source",
                 "source": false
               },
               "icon": "lucide-file",
-              "title": "9 - Universal Object"
+              "title": "9 - Consensus"
             }
           }
         ]
@@ -214,7 +214,7 @@
   "active": "aa7ed62f1bcd712a",
   "lastOpenFiles": [
     "Concurrent Systems/slides/class 9.pdf",
-    "Concurrent Systems/notes/9 - Universal Object.md",
+    "Concurrent Systems/notes/9 - Consensus.md",
     "Concurrent Systems/notes/8 - Enhancing Liveness Properties.md",
     "Concurrent Systems/notes/3b - Aravind's algorithm and improvements.md",
     "Concurrent Systems/notes/4 - Semaphores.md",
diff --git a/Concurrent Systems/notes/9 - Universal Object.md b/Concurrent Systems/notes/9 - Consensus.md
similarity index 75%
rename from Concurrent Systems/notes/9 - Universal Object.md
rename to Concurrent Systems/notes/9 - Consensus.md
index 4061611..fe4c083 100644
--- a/Concurrent Systems/notes/9 - Universal Object.md	
+++ b/Concurrent Systems/notes/9 - Consensus.md	
@@ -16,4 +16,8 @@ We focus on types whose operations are:
 
 An object of type $T_{U}$ is **universal** if every other object can be wait-free implemented using only objects of type $T_U$ and atomic R/W registers.
 
-This object is a **consensus object**: a *one-shot object* (every process c)
\ No newline at end of file
+This object is a **consensus object**: a *one-shot object* (every process can access it at most once) that provides only one operation `propose(v)` such that:
+- **Validity:** the returned value (or *decided value*) is one of the arguments of the propose (*proposed value*) in one invocation done by a process (*participant*)
+- **Integrity:** every process decides at most once
+- **Agreement:** the decided value is the same for all processes
+- **Wait-freedom:** every invocation of propose by a correct process terminates
\ No newline at end of file