Homotopy Type Theory
Sierpinski space > history (Rev #1)
Contents
Definition
The Sierpinski space or is defined as the partial function classifier on the unit type?, or as the homotopy-initial $\sigma$-frame.
As a higher inductive-inductive type
The Sierpinski space is inductively generated by
- a term
- a binary operation
- a function
- a term
- a binary operation
and the partial order type family is simultaneously inductively generated by
-
a family of dependent terms
representing that each type is a proposition.
-
a family of dependent terms
representing the reflexive property of .
-
a family of dependent terms
representing the transitive property of .
-
a family of dependent terms
representing the anti-symmetric property of .
-
a family of dependent terms
representing that is initial in the poset.
-
three families of dependent terms
representing that is a coproduct in the poset.
-
two families of dependent terms
representing that is a denumerable/countable coproduct in the poset.
-
a family of dependent terms
representing that is terminal in the poset.
-
three families of dependent terms
representing that is a product in the poset.
-
a family of dependent terms
representing the countably infinitary distributive property.
See also
References
Revision on March 12, 2022 at 05:51:28 by
Anonymous?.
See the history of this page for a list of all contributions to it.