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seen Feb 20 at 3:29

Feb
20
comment Analogues of Primitive Recursive Functions
I'm afraid that I don't follow either. What exactly are you saying you can rule out?
Feb
19
awarded  Nice Question
Jan
28
comment Analogues of Primitive Recursive Functions
@Ulrik That paper looks quite relevant, but not exactly what I'm looking for. If I'm reading it right, it seems to be about functions whose totality is provable using very weak set-theoretic assumptions, analogous to the characterization of primitive recursive functions as those functions which are provably total using very weak arithmetic assumptions. But I'm hoping for something which is specific to a fixed admissible set $A$, and specializes to primitive recursive arithmetic when I take $A = HF$. (Something that would generalize PRA, rather than being analogous to PRA.)
Jan
28
comment Analogues of Primitive Recursive Functions
@Carlo It is relevant, but I am asking for something more refined: I want to consider not just which sets are $\Sigma_1$-definable in $A$, but when $A$ "knows" that one $\Sigma_1$-set is contained in another.
Jan
21
asked Analogues of Primitive Recursive Functions
Jan
21
revised $(\infty, 1)$-Yoneda embedding via the Grothendieck construction
deleted 1 character in body
Jan
21
revised Lower Algebra: Modules over the monoidal category of abelian groups
added 200 characters in body
Jan
21
awarded  Enlightened
Jan
21
awarded  Nice Answer
Jan
20
answered What would be an infinity-groupoid analogue of the duality between sets and complete atomic boolean algebras?
Dec
31
awarded  Enlightened
Dec
31
awarded  Nice Answer
Nov
28
comment Failure of “equivariant triangulation” for finite complexes equipped with a $G$-action
Actually wait: I've misunderstood the question again, and what I said doesn't necessarily apply. (It applies when X comes from a finite object in the "genuine" equivariant category. But your finiteness condition looks like it might be weaker than that, even without allowing retracts.)
Nov
28
comment Failure of “equivariant triangulation” for finite complexes equipped with a $G$-action
Ah, misunderstood you. I don't have very much helpful to suggest, then. One comment: in the special case G = Z/p, if a space X with an action of G is to have the form you describe, then it satisfies the Sullivan conjecture. In particular, the homotopy fixed points for the action of G on the p-adic completion X_p must itself arise as the p-adic completion of a finite space. Possibly this could give you a way to test if something is a counterexample? (A finite X w/G action such that (X_p)^hG is not the p-adic completion of anything finite?)
Nov
28
comment Failure of “equivariant triangulation” for finite complexes equipped with a $G$-action
In Fun(BG,S), the orbits G/H generally won't be compact when H is nontrivial. But G itself generates the compact objects under finite colimits and retracts (this follows formally from the fact that it is a compact object which corepresents a conservative functor: in this case, the functor which forgets the G-action).
Oct
18
awarded  at.algebraic-topology
Oct
17
comment Associative Ring Spectra and Derived Completion
Let I be the fiber of the map A -> B. Then the fiber of the map A -> Tot^n is the (n+1)st smash power of I over A. For these fibers to vanish in the limit, it suffices that they are getting more connected. Since A is connective, it suffices for I to be connected, which is immediate from your hypothesis.
Oct
17
answered Associative Ring Spectra and Derived Completion
Oct
13
awarded  Good Answer
Oct
11
awarded  Enlightened