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

• wrote out parts of the proof of $\Omega^{un}_\bullet \simeq \pi_\bullet M O$ at Thom spectrum

• At crossed module it seems we are missing what i think should be the prototypical example: the relative second homotopy group $\pi_2(X,A)$ together with the bundary map $\delta:\pi_2(X,A)\to \pi_1(A)$ and the $\pi_1(A)$-action on $\pi_2(X,A)$. As someone confirms this example is correct I’ll add it to crossed module.

• Add basic definition in context of algebraic topology. My first contribution.

Grant

• Weakly reductive semigroups is a special class of semigroups that include monoids and is interesting from the perspective of being able to represent a semigroup as its translations.

• at the beginning of ring I have spelled out a more explicit definition. Also added the examples of rings on cyclic groups to explain the origin of the word “ring”.

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

• starting something – not done yet

• this is a bare sub-section, to be !include-ed into the pertinent entries (at embedding tensor, at tensor hierarchy and at super Lie algebra) in order to avoid having to copy this stuff around and to facilitate updating and syncing it across these entries

• Since I found out there is such a thing, I’d better start a page.

• following Zoran’s suggestion I added to the beginning of the Idea-section at monad a few sentences on the general idea, leading then over to the Idea with respect to algebraic theories that used to be the only idea given there.

Also added a brief stub-subsection on monads in arbitrary 2-categories. This entry deserves a bit more atention.

• Today I was asked for what I know about the development of the theory of Kan-fibrant simplicial manifolds. I realized that the nLab does not discuss this, so I have started a page now with the facts that come to mind right away. (Likely I forgot various things that should still be added.)

• I started an article about Martin-Löf dependent type theory. I hope there aren't any major mistakes!

One minor point: I overloaded $\mathrm{cases}$ by using it for both finite sum types and dependent sum types. Can anyone think of a better name for the operation for finite sum types?

• updated the link to her webpage.

• I added a section on strictification of pseudofunctors $C \to Cat$ to pseudofunctor, after seeing Finn and Mike respond to Karol in the stable monoidal derivator thread at the Café. The discussion is fairly sketchy and pedestrian. Also added a few references.

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

Anonymous

• The conjecture is not true for all single-sorted algebraic theories and this was known by Soviet mathematicians. I added a short high-level explanation on this and some references to translated works that have more detail. Presumably one should edit rest of the page (and references to it) to make it clear throughout that (i) the conjecture is false (ii) the general question “Which algebraic categories have the Higman property?” is still interesting (and potentially something category-theorists could study).

• started a Properties-section at Lawvere theory with some basic propositions.

Would be thankful if some experts looked over this.

Also added the example of the theory of sets. (A longer list of examples would be good!) And added the canonical reference.

• Edited the section on Boone conjecture in light of it being false.

• I added a couple of references for the claim

There is a Curry–Howard correspondence between linear-time temporal logic (LTL) and functional reactive programming (FRP).

How about for CLT and CLT* (in the computation tree logic section)?

Were we looking to integrate this section with the one above on temporal type theory as an adjoint logic, could there be a way via some branching representation of our type $Time$ as a tree?

I see Joachim Kock has an interesting way of presenting trees.

• The induced map most likely isn’t a homeomorphism when $X, Y$ are locally compact Hausdorff.

The original statement was in monograph by Postnikov without proof.

Not only that, in the current form it couldn’t possibly be true, since the map could lack to be bijective.

For more details see here: https://math.stackexchange.com/questions/3934265/adjunction-of-pointed-maps-is-a-homeomorphism .

I’ve added a reference in the case when $X, Y$ are compact Hausdorff though.

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