Not signed in (Sign In)

Not signed in

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

  • Sign in using OpenID

Site Tag Cloud

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 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 nforum 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 sheaves 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

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 19th 2010

    added a Properties-section to pullback

    • CommentRowNumber2.
    • CommentAuthorJohn Baez
    • CommentTimeJan 27th 2018
    • (edited Jan 27th 2018)

    I made some minor improvements to the Properties section of pullback, making it match the similar section in pushout insofar as it can. (It’s a bit tiring to have to look at both these pages to get all the basic properties, so I fixed that, but for properties that hold both for pullbacks and dually for pushouts I’m happy to have all the proofs at pullback - that’s how it works now.)

  1. Fixed a tiny typo ‘hold -> holds’.


    diff, v34, current

  2. Several pages on inductive types/W-types link to this page and use the term “pullback functor” with notation f *f^*, yet if you Ctrl-F on this page, you can’t find this term. This edit at least shortly mentions it and links to base change.

    Stipulation: redirect pullback functor to base change


    diff, v35, current

    • CommentRowNumber5.
    • CommentAuthorDmitri Pavlov
    • CommentTimeApr 6th 2020

    Added cartesian redirects.

    diff, v39, current

  3. Put some commutative diagrams in tikz-cd


    diff, v40, current

  4. Put some commutative diagrams in tikz-cd


    diff, v40, current

  5. Moved some commutative diagrams to tikz-cd


    diff, v40, current

  6. Thank you very much, Mr. or Mrs. Anonymous!

  7. Puts many diagrams in tikz-cd


    diff, v41, current

    • CommentRowNumber11.
    • CommentAuthorAlec Rhea
    • CommentTimeNov 4th 2020

    Added a spelled out definition of categorical pullbacks, not relying on an understanding of limits.

    diff, v42, current

    • CommentRowNumber12.
    • CommentAuthorDmitri Pavlov
    • CommentTimeNov 21st 2020

    Added a reference to Joyal’s CatLab.

    diff, v44, current

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeSep 4th 2021

    added pointer to:

    diff, v47, current