The Yoneda embedding for preadditive categories #
The Yoneda embedding for preadditive categories sends an object Y
to the presheaf sending an
object X
to the group of morphisms X ⟶ Y
. At each point, we get an additional End Y
-module
structure.
We also show that this presheaf is additive and that it is compatible with the normal Yoneda embedding in the expected way and deduce that the preadditive Yoneda embedding is fully faithful.
TODO #
- The Yoneda embedding is additive itself
The Yoneda embedding for preadditive categories sends an object Y
to the presheaf sending an
object X
to the End Y
-module of morphisms X ⟶ Y
.
Equations
- One or more equations did not get rendered due to their size.
Instances For
The Yoneda embedding for preadditive categories sends an object Y
to the presheaf sending an
object X
to the group of morphisms X ⟶ Y
. At each point, we get an additional End Y
-module
structure, see preadditiveYonedaObj
.
Equations
- One or more equations did not get rendered due to their size.
Instances For
The Yoneda embedding for preadditive categories sends an object X
to the copresheaf sending an
object Y
to the End X
-module of morphisms X ⟶ Y
.
Equations
- One or more equations did not get rendered due to their size.
Instances For
The Yoneda embedding for preadditive categories sends an object X
to the copresheaf sending an
object Y
to the group of morphisms X ⟶ Y
. At each point, we get an additional End X
-module
structure, see preadditiveCoyonedaObj
.
Equations
- One or more equations did not get rendered due to their size.
Instances For
Composing the preadditive yoneda embedding with the forgetful functor yields the regular Yoneda embedding.
Composing the preadditive yoneda embedding with the forgetful functor yields the regular Yoneda embedding.