michael/type-theory
2
0
Fork 0
Code Issues 21 Pull requests Projects 1 Releases 1 Packages Wiki Activity Actions

notes

Browse source
This commit is contained in:
Michael Zhang 2024-10-17 14:15:19 -05:00
parent 1a874e1e59
commit 3ff4ca9fc4
1 changed files with 9 additions and 9 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

18
notes/HLevels.md
View file

@ -1,20 +1,20 @@
# Properties
- Theorem 7.1.4:
- IF: $X$ is an $n$-type
- IF: $X$ is an $n$ type
- IF: $X \rightarrow Y$ is a retraction (has a left-inverse)
- THEN: $Y$ is an $n$-type
- THEN: $Y$ is an $n$ type
- Corollary 7.1.5:
- IF: $X \simeq Y$
- IF: $X$ is an $n$-type
- THEN: $Y$ is an $n$-type
- IF: $X$ is an $n$ type
- THEN: $Y$ is an $n$ type
- Theorem 7.1.7:
- IF: $X$ is an $n$-type
- THEN: it is also an $(n + 1)$-type
- IF: $X$ is an $n$ type
- THEN: it is also an $(n + 1)$ type
- Theorem 7.1.8:
- IF: $A$ is an $n$-type
- IF: $B(a)$ is an $n$-type for all $a : A$
- THEN: $\sum_{(x : A)} B(x)$ is an $n$-type
- IF: $A$ is an $n$ type
- IF: $B(a)$ is an $n$ type for all $a : A$
- THEN: $\sum_{(x : A)} B(x)$ is an $n$ type
## -2: Contractible