From 3ff4ca9fc48caa71dc0b13e2052ec09e409846b5 Mon Sep 17 00:00:00 2001 From: Michael Zhang Date: Thu, 17 Oct 2024 14:15:19 -0500 Subject: [PATCH] notes --- notes/HLevels.md | 18 +++++++++--------- 1 file changed, 9 insertions(+), 9 deletions(-) diff --git a/notes/HLevels.md b/notes/HLevels.md index 8138e22..b6b726a 100644 --- a/notes/HLevels.md +++ b/notes/HLevels.md @@ -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