Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory object of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

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)
   • PermaLink
   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
   • PermaLink
   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.