Processing math: 100%
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 definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite 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 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

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).
    • brief category:people-entry for hyperlinking references

      v1, current

    • I have begun cleaning up the entry cycle category, tightening up definitions and proofs. This should render some of the past discussion obsolete, by re-expressing the intended homotopical intuitions (in terms of degree one maps on the circle) more precisely, in terms of “spiraling” adjoints on the poset .

      Here is some of the past discussion I’m now exporting to the nForum:

      The cycle category may be defined as the subcategory of Cat whose objects are the categories [n]Λ which are freely generated by the graph 012n0, and whose morphisms Λ([m],[n])Cat([m],[n]) are precisely the functors of degree 1 (seen either at the level of nerves or via the embedding Ob[n]ΛR/ZS1 given by kk/(n+1)modZ on the level of objects, the rest being obvious).

      The simplex category Δ can be identified with a subcategory of Λ, having the same objects but with fewer morphisms. This identification does not respect the inclusions into Cat, however, since [n] and [n]Λ are different categories.

      diff, v27, current

    • Create page, add some initial references. Referenced from the ’category theory’ page.

      v1, current

    • starting page on impredicative polymorphism in dependent type theory

      Anonymouse

      v1, current

    • Inspired by a discussion with Martin Escardo, I created taboo.

    • starting disambiguation page on impredicative universes

      Anonymouse

      v1, current

    • I added this to the entry for Nima Arkani-Hamed.

      Urs (or anyone else) do you know anything about Nima’s recent interest in category theory?

      On Category Theory

      “six months ago, if you said the word category theory to me, I would have laughed in your face and said useless formal nonsense, and yet it’s somehow turned into something very important in my intellectual life in the last six months or so” (@ 44:05 in The End of Space-Time July 2022)

    • Added work on Ologs and started restructuring the page

      rTuyeras

      diff, v5, current

    • have created enriched bicategory in order to help Alex find the appropriate page for his notes.

    • gave this reference item some more hyperlinks:

      • Michael Atiyah, Ian G. Macdonald, Introduction to commutative algebra, (1969, 1994) [pdf, ISBN:9780201407518]

      diff, v16, current

    • Categories enriched over groupoid form strict (2,1) categories. Edited for clarity.

      Mark Williams

      diff, v4, current

    • I strongly disagree with the statement in Grothendieck category that the Grothendieck category is small. The main examples like RMod are not! What did the writer of that line have in mind ?

    • I added to the “abstract nonsense” section in free monoid a helpful general observation on how to construct free monoids. “Adjoint functor theorem” is overkill for free monoids over Set.

    • brief category:people-entry for hyperlinking references

      v1, current

    • starting stub on gaseous vector spaces

      Anonymouse

      v1, current

    • I have created lax morphism, with general definitions and a list of examples. It would be great to have more examples.

    • Created a stub page for this concept, which surprisingly didn’t exist yet.

      v1, current

    • starting article on set truncations

      Anonymouse

      v1, current

    • copying text from HoTT wiki

      Anonymous

      v1, current

    • I have added some things to frame. Mostly duplicating things said elsewhere (at locale and at (0,1)-topos), but I need these statements to be at frame itself.

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

      Anonymous

      v1, current

    • Clarify that the impredicative definition only quantifies over truth values.

      diff, v18, current

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

      Anonymous

      v1, current

    • At overt space there was a remark that since the definition quantifies over “spaces”, the overtness of a single space might depend on the general meaning chosen for “space”, but that no example was known to the author. I added an example involving synthetic topology, which may not be quite what the author of that remark was thinking of, but which I think is interesting.

    • There has GOT to be a better photograph than that! Is there anyone here in Oxford? Can they go and get a picture for us?

    • Treated the case of comodules over corings, which differs from the definition for internal comonoids, though coring is an internal monoid. Namely, comodules over corings are defined as modules with coaction, rather than bimodules with coaction.

      diff, v16, current

    • I made some very minor changes to the introduction at descent. I hesitate to do more but at present the discussion does not seem that readable to me. Can someone look at it to see what they think? The intro seems to plunge in deep very quickly and so the ‘idea’ of descent as that of gluing local information together, does not come across to me. The article is lso quite long and perhaps needs splitting up a bit.

    • Added some content to display map from Taylor’s book. Not very deep, mostly as a reference to the respective section for me.

    • added a bare minimum sentence to the (previously empty) Idea-section, and more references

      diff, v4, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • The adeles are not the Cartesian product, but the restricted product.

      Reed

      diff, v15, current

    • Created a page Morava K-theory . A lot to add. Will fill out later, with better reference list. Please edit!
    • Mathematician of the turn of 19/20th century.

      v1, current