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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.
   • CommentAuthorfastlane69
   • CommentTimeAug 4th 2016
   • (edited Aug 4th 2016)
   • PermaLink
   Author: fastlane69
   Format: MarkdownItexAs I'm being introduced and learning about these theories, I wanted to ask your help in putting things in perspective. My impression at the moment is that Type is a more abstract theory than Category and that Topos is a more specific theory than Category. And when I say abstract, I'm getting the impression that I could phrase that as a theory with many axioms and few derivations where when I say specific I'm getting the impression that I could phrase that to mean few axioms and many derivations Are these impressions accurate? If so, where does HoTT fit on this scale?

   As I’m being introduced and learning about these theories, I wanted to ask your help in putting things in perspective.

   My impression at the moment is that Type is a more abstract theory than Category and that Topos is a more specific theory than Category.

   And when I say abstract, I’m getting the impression that I could phrase that as a theory with many axioms and few derivations where when I say specific I’m getting the impression that I could phrase that to mean few axioms and many derivations

   Are these impressions accurate?

   If so, where does HoTT fit on this scale?