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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 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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure 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 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.
   • CommentAuthorAli Caglayan
   • CommentTimeSep 6th 2018
   • PermaLink
   Author: Ali Caglayan
   Format: MarkdownItexThis page needs some fleshing out. I will try to come back later and add some more content. <a href="https://ncatlab.org/homotopytypetheory/revision/diff/higher+inductive+type/9">diff</a>, <a href="https://ncatlab.org/homotopytypetheory/revision/higher+inductive+type/9">v9</a>, <a href="https://ncatlab.org/homotopytypetheory/show/higher+inductive+type">current</a>

   This page needs some fleshing out. I will try to come back later and add some more content.

   diff, v9, current

2. • CommentRowNumber2.
   • CommentAuthorAli Caglayan
   • CommentTimeOct 10th 2018
   • PermaLink
   Author: Ali Caglayan
   Format: MarkdownItexAdded a working list of HITs, I have also included the references from the nlab. This will need to be cleaned up later. The idea is that each of the HITs will have their own articles detailing their inference rules and other properties. This article should also discuss the disparity between judgemental and propositional equality for the higher computation rules. As far as I know there is not much literature on this. <a href="https://ncatlab.org/homotopytypetheory/revision/diff/higher+inductive+type/10">diff</a>, <a href="https://ncatlab.org/homotopytypetheory/revision/higher+inductive+type/10">v10</a>, <a href="https://ncatlab.org/homotopytypetheory/show/higher+inductive+type">current</a>

   Added a working list of HITs, I have also included the references from the nlab. This will need to be cleaned up later. The idea is that each of the HITs will have their own articles detailing their inference rules and other properties.

   This article should also discuss the disparity between judgemental and propositional equality for the higher computation rules. As far as I know there is not much literature on this.

   diff, v10, current