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Apr
19
revised Difficulties with descent data as homotopy limit of image of Čech nerve
added 3 characters in body
Apr
7
comment Is the analytification functor part of a geometric morphism of topoi?
I don't deal with analytic spaces, but this kind of thing is considered in my thesis. Preservation of finite limits is not necessary if you are willing to give up having a geometric morphism.
Apr
6
answered Posets (partially ordered sets) in equational logic
Mar
31
comment Relative version of Quillen's theorem A
Isn't this Grothendieck's version? See Théorème 2.1.13 in [Cisinski, 2003, Le localisateur fondemental minimal].
Mar
31
answered Reedy model structure on sSet
Mar
29
comment Self-enrichment of reflective subcategories of self-enriched categories
Perhaps you are looking for the concept of an exponential ideal.
Mar
24
comment Stability of adjunctions of infinity-categories by base change
@DylanWilson A priori, you only know that you have an adjunction where the left adjoint is what you want – what about the right adjoint?
Mar
16
awarded  Necromancer
Mar
8
revised Direct limit closure of Serre subcategories
edited tags
Mar
7
comment Model category of cofibrant topological spaces
Are the morphisms the same?
Feb
20
comment Is the hom-simplicial set in the hammock localization a nerve?
In §35 of the final version, they discuss a Grothendieck construction, use it to build a 2-category, and show that it is weakly equivalent to the hammock localisation. As far as I understand it, it boils down to Thomason's homotopy colimit theorem and the fact that hom-spaces of the hammock localisation are colimits of Reedy-cofibrant diagrams.
Feb
20
comment Is the hom-simplicial set in the hammock localization a nerve?
In fact, in DHKS, they construct precisely such a 2-category as a model for simplicial localisation.
Feb
19
comment Is the hom-simplicial set in the hammock localization a nerve?
It is definitely not the nerve of a groupoid. If it were then $(\infty, 1)$-categories would be the same as $(2, 1)$-categories.
Feb
16
comment Free Objects in Functor Categories
Small matters. Abelian is what is asked for.
Feb
12
comment Seeking more information regarding the “rigoidal category” of $\mathbb{N}$-graded sets
The Lawvere theory version is the same. The free cartesian monoidal category on one object is $\mathbf{FinSet}^\mathrm{op}$, and the presheaf category $[\mathbf{FinSet}, \mathbf{Set}]$ has a composition monoidal structure in which the monoids are Lawvere theories. Equivalently, one could observe that $[\mathbf{FinSet}, \mathbf{Set}]$ is equivalent to the monoidal category of endofunctors on $\mathbf{Set}$ that preserve filtered colimits, and then go via accessible monads.
Feb
8
awarded  Nice Answer
Feb
8
asked Flat + locally of finite presentation + monomorphism = open immersion
Feb
4
awarded  Enlightened
Feb
4
comment A nice subcategory of the category of measurable spaces
In situations like this we should a class-locally presentable pretopos. I'm not so sure whether we get a cartesian closed category, or even whether we get a subobject classifier. Restricting to a small "subsite" (not standard terminology) would give a Grothendieck topos but it seems like an arbitrary thing to do.
Feb
4
comment A nice subcategory of the category of measurable spaces
I suppose coaccessibility is what we want, though. Small presheaves on an coaccessible categories are the same as (covariant) accessible functors, if I recall correctly. On the other hand, restricting to small sheaves is not going to give you a Grothendieck topos...