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1. • CommentRowNumber1.
   • CommentAuthorMike Shulman
   • CommentTimeJul 25th 2016
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexI ran across a reference (I think in Lambek & Scott) to a use of the word "dogma" for a kind of category (context suggests it was something from which one can generate a topos, perhaps by some kind of exact completion). Does anyone know a reference for this?

   I ran across a reference (I think in Lambek & Scott) to a use of the word “dogma” for a kind of category (context suggests it was something from which one can generate a topos, perhaps by some kind of exact completion). Does anyone know a reference for this?

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeJul 25th 2016
   • (edited Jul 25th 2016)
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   Author: David_Corfield
   Format: MarkdownItex>The construction of the topos generated by a dogma follows Volger... 'From types to sets', Joachim Lambek, doi:10.1016/0001-8708(80)90013-4 So 28. H. VOLGER, “Completeness Theorem for Logical Categories, pp. 51-86, Lecture Notes in Mathematics No. 445, Springer-Verlag, Berlin/New York, 1975. 29. H. VOLGER, “Logical and Semantical Categories and Topoi,” pp. 87-100, Lecture Notes in Mathematics No. 445, Springer-Verlag, Berlin/New York, 1975.

   The construction of the topos generated by a dogma follows Volger…

   ’From types to sets’, Joachim Lambek, doi:10.1016/0001-8708(80)90013-4

   So

   1. H. VOLGER, “Completeness Theorem for Logical Categories, pp. 51-86, Lecture Notes in Mathematics No. 445, Springer-Verlag, Berlin/New York, 1975.

   2. H. VOLGER, “Logical and Semantical Categories and Topoi,” pp. 87-100, Lecture Notes in Mathematics No. 445, Springer-Verlag, Berlin/New York, 1975.

3. • CommentRowNumber3.
   • CommentAuthorDavid_Corfield
   • CommentTimeJul 25th 2016
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexThe Lambek [article](http://ac.els-cdn.com/0001870880900134/1-s2.0-0001870880900134-main.pdf?_tid=e90b931e-52a1-11e6-adef-00000aab0f02&acdnat=1469476783_75b86ea355a387b0fe0cdd8db8bdaeeb) looks interesting: >The present author became interested in an equational approach to foundations and, at the Halifax conference in 1971, proposed the name “dogma” for certain structured categories which were related to type theory a la Church as toposes are related to set theory: dogmas/type theory = toposes/set theory.

   The Lambek article looks interesting:

   The present author became interested in an equational approach to foundations and, at the Halifax conference in 1971, proposed the name “dogma” for certain structured categories which were related to type theory a la Church as toposes are related to set theory: dogmas/type theory = toposes/set theory.

4. • CommentRowNumber4.
   • CommentAuthorMike Shulman
   • CommentTimeJul 25th 2016
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   Author: Mike Shulman
   Format: MarkdownItexThanks! Volger's articles are paywalled, but Lambek's has the definition. It looks like roughly a [[tripos]] for which the fiberwise structure is representable by operations on the classifier, so that the whole thing can be defined as a category with structure without taking the fibration as extra data.

   Thanks! Volger’s articles are paywalled, but Lambek’s has the definition. It looks like roughly a tripos for which the fiberwise structure is representable by operations on the classifier, so that the whole thing can be defined as a category with structure without taking the fibration as extra data.