Re: The relevance of category and topos theory

From: Wei Dai <>
Date: Thu, 18 Jul 2002 10:19:26 -0700

On Sun, Jul 07, 2002 at 11:25:28AM -0700, Tim May wrote:
> "Topos Theory, spring term 1999
> "A graduate course (6 course points) in mathematical logic.
> ------------------------------------------------------------------------
> "Topos theory grew out of the observation that the category of sheaves
> over a fixed topological space forms a universe of "continuously
> variable sets" which obeys the laws of intuitionistic logic. These sheaf
> models, or Grothendieck toposes, turn out to be generalisations of
> Kripke and Beth models (which are fundamental for various non-classical
> logics) as well as Cohen's forcing models for set theory. The notion of

I've been reading _Conceptual Mathematics_ but so far have not seen many
connections with topics I'm most interested in learning right now (logic,
recursion theory, decision theory). Perhaps category theory is more
relevant in physics, or I should move on to topos theory.

Topos theory seems to be motivated by intuitionistic logic, which is
considered the logical basis of constructive mathematics (according to Does that mean I
should learn something about intuitionistic logic and constructivism first
before trying to tackle topos theory?

I notice the book "Constructivism in Mathematics" by Troelstra and Dalen.
Has anyone here read it, or can anyone recommend another book?
Received on Thu Jul 18 2002 - 10:20:08 PDT

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