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1d

revised 
Is an open map with open relative diagonal necessarily a local homeomorphism?
edited tags 
1d

comment 
The bifunctoriality of co/limits
The short answer is: derivators. 
2d

comment 
Applications of set theory in physics
Isn't that the controversial Chaos, Solitons & Fractals? 
Mar 25 
comment 
is sufficient cohesion equivalent to the connectedness of subobject classifier?
I don't understand your question. The subobject classifier always acts on the partial map representor. 
Mar 25 
comment 
Relationship between coherent toposes/coherent logic and coherent sheaves
The definition of coherent topos is built on the definition of coherent object, which is essentially the same as the definition of coherent sheaf. 
Mar 23 
asked  Is an open map with open relative diagonal necessarily a local homeomorphism? 
Mar 14 
comment 
Parodies of abstruse mathematical writing
Not quite writing per se, but perhaps relevant. 
Mar 13 
revised 
Canonical colimit and cartesian product of simplicial sets
edited tags 
Mar 13 
answered  Canonical colimit and cartesian product of simplicial sets 
Mar 3 
comment 
Cartesian products between cofibrant simplicial presheaves
Yes, it does seem to carry over. 
Mar 3 
comment 
Definition of internal field objects
@მამუკაჯიბლაძე No, I don't think Martin's definition is especially similar to the notion of geometric field (which nLab calls "discrete field"). It's much closer to the definition via axiom F2. 
Mar 3 
comment 
Definition of internal field objects
It appears to me your definition is a translation of "$x$ is invertible in a field if and only if $x \ne 0$", where you have interpreted $x \ne 0$ using the notion of a complementary subobject. This is a natural definition, I suppose. 
Feb 23 
comment 
Subdivision of a small category
You are correct: the nerve of the category in question has infinitely many nondegenerate simplices. 
Feb 20 
answered  Cartesian products between cofibrant simplicial presheaves 
Feb 20 
comment 
Cartesian products between cofibrant simplicial presheaves
So, you are assuming $\mathcal{C}$ has products? 
Feb 19 
comment 
homotopy tensor product of functors and bar construction
Short answer to final question: yes, the bar construction computes homotopy weighted colimits. 
Feb 14 
comment 
Does homotopy invariance of homology follow from the structure of the simplex category $\Delta$?
Hmmm. I don't think it's necessarily true that $S_\bullet (F \Delta^n)$ is always contractible. That would imply that the coequaliser of $\mathcal{C} (F \Delta^1, F \Delta^n) \rightrightarrows \mathcal{C} (F \Delta^0, F \Delta^n)$ is a singleton, but that's not true in general. (The simplest example is to take $F$ constant with value an object in $\mathcal{C}$ with more than one endomorphism. I don't know how to construct an example where $F \Delta^0$ is terminal.) 
Feb 14 
comment 
Does homotopy invariance of homology follow from the structure of the simplex category $\Delta$?
Yes, I'd rather think about the "singular simplicial set" than pass directly to chains. Then it's much easier to see that simplicial homotopies go to simplicial homotopies, and everything else is as for simplicial homology. I don't follow what you say about cosimplicial resolutions, though. 
Feb 14 
comment 
Does homotopy invariance of homology follow from the structure of the simplex category $\Delta$?
You write $\times$ but work in the category of simplicial abelian groups. Do you mean $\otimes$ instead? Either way, what does $\Delta^1 \times ()$ mean? 
Feb 13 
comment 
The groupoid of algebraic expressions and proofs
Look up higher inductive types in homotopy type theory. 