Not signed in (Sign In)

Start a new discussion

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 bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory 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 finite foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity 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 itex k-theory lie lie-theory limit 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 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 science set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory string string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory 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).
    • I have incorporated Jonas’ comment into the text at pretopos, changing the definition to “a category that is both exact and extensive”, as this is sufficient to imply that it is both regular and coherent.

    • Add some discussion of the equivalence between the two definitions, and how in practice we usually use the family-of-collections-of-morphisms one.

      diff, v70, current

    • I think the line between the two types of Kan extension (weak versus pointwise) is drawn at the wrong place. Am I missing something?

    • for completeness (prompted by opetopic type theory) I started an entry opetopic omega-category.

      For me presently this just serves to purpose to record Thorsten Palm’s definition of opetopic omega-category, as I understand it from what Eric Finster tells me.

      For the definitions by Baez-Dolan and by Makkai the entry presently only contains placeholders, please feel invited to fill in detail.

      All these definitions consider opetopic sets. The difference is in which structure and property is put on that. The original definition of universal cells is somewhat involved, as far as I see. Palm’s definition is of a nice straightforward homotopy-theoretic flavor. It seems plausible that this definition satisfies the homotopy hypothesis, but I don’t know if anyone looked into it.

      Accoring to Eric Finster, Palm showed that his definition is a special case of Makkai’s, but the converse remains open.

    • Stack entry says: "The notion of stack is the one-step vertical categorification of a sheaf." In Grothendieck's main works, like pursuing stacks and in the following works of French schools, stack is any-times categorification of a sheaf, and the one-step case is called more specifically 1-stack. We can talk thus about stack in narrow sense or 1-stacks and stacks in wider sense as n-stacks for all n. Topos literature mainly means that the stack is the same as internal 1-stack.

    • Page created, but author did not leave any comments.

      v1, current

    • I’ve removed this query box from metric space and incorporated its information into the text:

      Mike: Perhaps it would be more accurate to say that the symmetry axiom gives us enriched \dagger-categories?

      Toby: Yeah, that could work. I was thinking of arguing that it makes sense to enrich groupoids in any monoidal poset, cartesian or otherwise, since we can write down the operations and all equations are trivial in a poset. But maybe it makes more sense to call those enriched \dagger-categories.

    • Used ˜\tilde \mathbb{C} for the name of the indexed category

      Bartosz Milewski

      diff, v18, current

    • Since I gathered them for my recent talk, I may as well provide a list here of work in this area. I need to add names, etc.

      v1, current

    • An attempt to create this page was made by Paulo Perrone, but the creation was not successful. Am creating the page without any content beyond ’TODO’ now as a test.

      v1, current

    • I have expanded the Idea-section at moduli stack of elliptic curves, have tried to add more pertinent references, and have touched the subsection on “Over general rings” and on the derived version.

      In the course of this I started to split off some entries such as nodal cubic curve (which now has a little bit of content) and cuspidal cubic curve (which does not yet).

    • I have added to Teichmüller theory a mini-paragraph Complex structure on Teichmüller space with a minimum of pointers to the issue of constructing a complex structure on Teichmüller space itself.

      Maybe somebody has an idea on the following: The Teichmüller orbifold itself should have a neat general abstract construction as the full subobject on the étale maps of the mapping stack formed in smooth \infty-groupoids/smooth \infty-stacks into the Haefliger stack for complex manifolds : via Carchedi 12, pages 37-38.

      Might we have a refinement of this kind of construction that would produce the Teichmüller orbifold directly as on objects in \infty-stacks over the complex-analytic site?

    • Switch commuting reasoning to use an implication for clarity.

      diff, v19, current

    • I think that this should have linked to ’variety of algebras’ instead of ’algebraic variety’.

      diff, v20, current

    • Page created, but author did not leave any comments.

      v1, current

    • I have added pdf-links to the reference

      and promoted this to the top of the list, since I suppose this is the most comprehensive account that a reader might want to go to first. Will also edit accordingly at topological stack

      diff, v18, current

    • I replaces the “?” by “Č” (including redirects). I hope this was the correct thing to do.

      diff, v18, current

    • In discrete fibration I added a new section on the Street’s definition of a discrete fibration from AA to BB, that is the version for spans of internal categories. I do not really understand this added definition, so if somebody has comments or further clarifications…

    • starting something, for the moment mainly to record references

      v1, current

    • starting something, for the moment mainly to record references

      v1, current