From: "Валерий Исаев" <"valery..."@gmail.com>
To: Homotopy Type Theory <HomotopyT...@googlegroups.com>
Subject: Connected 1-Types
Date: Mon, 31 Oct 2016 07:42:05 -0700 (PDT) [thread overview]
Message-ID: <a5f9acf7-e01e-48be-92b1-720d1bb316a9@googlegroups.com> (raw)
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Hello, everybody,
The following questions have bothered me for some time now.
Let's consider the type of pointed connected 1-types, that is PC1T = Σ (A :
1-Type) (a₀ : A) (isConnected A), where isConnected A = (a a' : A) → ∥ a ≡
a' ∥.
This type is equivalent to the type of groups (this construction uses
HITs). This implies that it is a 1-type.
Is there a way to prove directly (without HITs) that PC1T is a 1-type?
Also, is it true for the type of connected 1-types (C1T = C1T = Σ (A :
1-Type) (isConnected A)) or merely inhabited connected 1-types (IC1T = Σ (A
: 1-Type ) (∥ A ∥ × isConnected A))?
Are there analogous theorems for n-types with n > 1?
Regards,
Valery Isaev
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next reply other threads:[~2016-10-31 14:42 UTC|newest]
Thread overview: 3+ messages / expand[flat|nested] mbox.gz Atom feed top
2016-10-31 14:42 Валерий Исаев [this message]
2016-10-31 15:00 ` Ulrik Buchholtz
2016-10-31 15:15 ` [HoTT] " Joyal, André
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