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1. • CommentRowNumber1.
   • CommentAuthorDavid_Corfield
   • CommentTimeJan 19th 2015
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   Author: David_Corfield
   Format: MarkdownItexSomeone just started [[relation between type theory and topology]], referring to a talk by Martin Escardo.

   Someone just started relation between type theory and topology, referring to a talk by Martin Escardo.

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeJan 19th 2015
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   Author: Mike Shulman
   Format: MarkdownItexThanks for the pointer! I've tried to bring the POV in line a bit. I also deleted the comment "this may hint at an extension to computational trinitarianism" because I feel that this fits squarely inside the existing framework of CT, namely on the categorical side.

   Thanks for the pointer! I’ve tried to bring the POV in line a bit.

   I also deleted the comment “this may hint at an extension to computational trinitarianism” because I feel that this fits squarely inside the existing framework of CT, namely on the categorical side.

3. • CommentRowNumber3.
   • CommentAuthorspitters
   • CommentTimeJan 19th 2015
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   Author: spitters
   Format: MarkdownItexThe relation to type theory needs to be clarified a bit. Some of these ideas go back to Smyth, Abramsky and Vickers in [[domain theory]] and geometric logic. There is also Paul Taylor's [[abstract Stone duality]]. However, usually the type theory is rather weak as it needs to be interpreted in a category of topological spaces or locales. Martin's work of connecting this to MLTT is work in progress. A similar confusion is present in [[geometric type theory]].

   The relation to type theory needs to be clarified a bit.

   Some of these ideas go back to Smyth, Abramsky and Vickers in domain theory and geometric logic.

   There is also Paul Taylor’s abstract Stone duality.

   However, usually the type theory is rather weak as it needs to be interpreted in a category of topological spaces or locales. Martin’s work of connecting this to MLTT is work in progress.

   A similar confusion is present in geometric type theory.