diff --git a/hott/init/default.hlean b/hott/init/default.hlean
index aa59f39a7..1cbeb2a5f 100644
--- a/hott/init/default.hlean
+++ b/hott/init/default.hlean
@@ -7,3 +7,4 @@ Authors: Leonardo de Moura
 prelude
 import init.datatypes init.reserved_notation init.tactic init.logic
 import init.bool init.num init.priority init.relation init.wf init.prod
+import init.sigma
diff --git a/hott/init/sigma.hlean b/hott/init/sigma.hlean
new file mode 100644
index 000000000..8b2c55f70
--- /dev/null
+++ b/hott/init/sigma.hlean
@@ -0,0 +1,25 @@
+/-
+Copyright (c) 2014 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura, Jeremy Avigad, Floris van Doorn
+-/
+prelude
+import init.num init.wf init.logic init.tactic
+
+structure sigma {A : Type} (B : A → Type) :=
+dpair :: (dpr1 : A) (dpr2 : B dpr1)
+
+notation `Σ` binders `,` r:(scoped P, sigma P) := r
+
+namespace sigma
+
+  notation `dpr₁` := dpr1
+  notation `dpr₂` := dpr2
+
+  namespace ops
+  postfix `.1`:(max+1) := dpr1
+  postfix `.2`:(max+1) := dpr2
+  notation `⟨` t:(foldr `,` (e r, sigma.dpair e r)) `⟩`:0 := t --input ⟨ ⟩ as \< \>
+  end ops
+
+end sigma