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 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.
   • CommentAuthorUrs
   • CommentTimeJan 20th 2023
   • (edited Jan 20th 2023)
   • PermaLink
   Author: Urs
   Format: MarkdownItexNow that we have an entry *[[dependent function]]*, I feel it's time to showcase also the corresponding notation $$ f \;\,\colon\;\, (d \,\colon\, D) \to C_d $$ for $$ f \,\colon\, \underset{d \,\colon\, D}{\prod} \, C_d $$ and dually for dependent pairs; and to cross-link all these notions at a glance. So I am hereby making a little [table](https://ncatlab.org/nlab/show/dependent+functions+and+dependent+pairs+--+table), meant to be `!include`-d into the "Related concepts"-sections of the relevant entries. (Currently the table says "dependent co-product" for what everyone calls the "dependent sum". I can change that if there is much insistence that I should, and I know it's an uphill battle, but it bugs me that saying "dependent sum" for the dependent coproduct was a step in the wrong direction.) <a href="https://ncatlab.org/nlab/revision/dependent+functions+and+dependent+pairs+--+table/1">v1</a>, <a href="https://ncatlab.org/nlab/show/dependent+functions+and+dependent+pairs+--+table">current</a>

   Now that we have an entry dependent function, I feel it’s time to showcase also the corresponding notation

   $$f \;\,\colon\;\, (d \,\colon\, D) \to C_d$$

   for

   $$f \,\colon\, \underset{d \,\colon\, D}{\prod} \, C_d$$

   and dually for dependent pairs; and to cross-link all these notions at a glance.

   So I am hereby making a little table, meant to be !include-d into the “Related concepts”-sections of the relevant entries.

   (Currently the table says “dependent co-product” for what everyone calls the “dependent sum”. I can change that if there is much insistence that I should, and I know it’s an uphill battle, but it bugs me that saying “dependent sum” for the dependent coproduct was a step in the wrong direction.)

   v1, current