User Francesco Genovese

9 votes

1 answer

1k views

Is it possible to make an autoequivalence of categories an automorphism?

asked Mar 22, 2012 at 11:29

8 votes

3 answers

544 views

Example: a pair of nonisomorphic parallel morphisms with isomorphic cones

asked Jan 21, 2013 at 14:51

7 votes

2 answers

723 views

Do weak equivalences in a model category admit a calculus of fractions?

asked Feb 16, 2012 at 14:07

7 votes

0 answers

264 views

Is the bar resolution of complexes dg-functorial?

asked Jun 3, 2016 at 20:26

7 votes

2 answers

381 views

The correct homotopically relevant notion of ideals of dg-algebras (or $\mathbb E_1$-rings)

asked May 28, 2020 at 12:43

6 votes

1 answer

822 views

About the definition of quasi-equivalent dg-categories

asked Mar 4, 2012 at 16:05

6 votes

1 answer

357 views

$A_\infty$-categories and their equivalent dg-categories: the case of $\mathcal{RH}om(\mathcal A,\mathcal B)$

asked Dec 5, 2012 at 15:46

6 votes

1 answer

635 views

Pullbacks and pushouts in the category of (small) dg-categories

asked Feb 20, 2013 at 18:42

6 votes

1 answer

256 views

Good properties of the $H^0$ functor (from quasi-functors to ordinary functors)

asked Jul 18, 2014 at 21:05

6 votes

2 answers

1k views

A general theory of quasi-functors, generalizing from dg-categories to $\mathcal V$-categories, with $\mathcal V$ monoidal model category

asked Aug 8, 2014 at 21:02

6 votes

2 answers

383 views

If $A$ is a cofibrant commutative dg-algebra over a commutative ring of characteristic $0$, then its underlying chain complex is cofibrant

asked Jul 24, 2020 at 9:57

6 votes

1 answer

348 views

The category of complexes over a dg-algebra is Grothendieck (it has a generator)

asked Jun 4, 2019 at 10:00

5 votes

0 answers

199 views

Lifting commutative diagrams of functors from the homotopy level to the "higher" level

asked Aug 13, 2014 at 21:10

5 votes

1 answer

1k views

Cohomology of derived tensor product of complexes and Künneth spectral sequence

asked Jun 5, 2020 at 13:19

5 votes

0 answers

275 views

When does the canonical model structure on $\mathcal V$-$\mathbf{Cat}$ give a structure of monoidal model category?

asked Mar 3, 2015 at 14:18

4 votes

1 answer

799 views

(Homotopy) limits and colimits in a dg-category

asked Aug 7, 2014 at 10:34

4 votes

0 answers

191 views

The definition of flat sheaves of rings on algebraic stacks

asked Jun 12, 2020 at 20:02

4 votes

0 answers

217 views

Natural transformations of $A_\infty$-functors (between dg-categories) are "directed homotopies" (reference?)

asked Aug 24, 2015 at 19:53

4 votes

0 answers

188 views

Can cofibrant replacements of k-linear categories in dg-cat be found k-linear?

asked Jan 25, 2012 at 22:27

4 votes

2 answers

218 views

When is a triangulated category uniquely determined by its generators?

asked May 7, 2014 at 8:56

4 votes

2 answers

421 views

Universal property of gluing [collage, cograph] of dg-categories

asked May 13, 2014 at 10:18

3 votes

1 answer

252 views

Taking zeroth cohomology of a dg-module over a dg-category is "good" on representables, but probably "bad" on cones

asked Aug 7, 2014 at 9:16

3 votes

1 answer

232 views

Reconstructing a morphism of exact triangles in the homotopy cat. of a dg-cat. using a "functorial cone map"

asked Aug 5, 2014 at 13:40

3 votes

0 answers

112 views

Coverings of (DM) stacks and categories of descent data

asked Jun 2, 2020 at 20:00

3 votes

1 answer

149 views

Morphisms $P \to M$ in the derived category of a dg-category, if $P$ is h-projective

asked May 22, 2015 at 19:15

3 votes

1 answer

566 views

Comparing the definitions of perfect complexes on algebraic stacks and schemes

asked Oct 10, 2016 at 17:04

3 votes

1 answer

432 views

K-injective (also known as hoinjective) complexes of sheaves of modules

asked Jan 10, 2017 at 17:35

2 votes

0 answers

529 views

The derived pushforward between derived categories of twisted sheaves preserves (possibly infinite) direct sums

asked Feb 8, 2017 at 16:32

2 votes

0 answers

58 views

Comparing right and left quasi-representable bimodules

asked Apr 24, 2015 at 17:11

2 votes

0 answers

169 views

if $I$ is finitely presented nilpotent and $M/IM$ is finitely presented, then $M$ is finitely presented

asked Jun 25, 2020 at 12:00

Stack Exchange Network

41 Questions

Is it possible to make an autoequivalence of categories an automorphism?

Example: a pair of nonisomorphic parallel morphisms with isomorphic cones

Do weak equivalences in a model category admit a calculus of fractions?

Is the bar resolution of complexes dg-functorial?

The correct homotopically relevant notion of ideals of dg-algebras (or $\mathbb E_1$-rings)

About the definition of quasi-equivalent dg-categories

$A_\infty$-categories and their equivalent dg-categories: the case of $\mathcal{RH}om(\mathcal A,\mathcal B)$

Pullbacks and pushouts in the category of (small) dg-categories

Good properties of the $H^0$ functor (from quasi-functors to ordinary functors)

A general theory of quasi-functors, generalizing from dg-categories to $\mathcal V$-categories, with $\mathcal V$ monoidal model category

If $A$ is a cofibrant commutative dg-algebra over a commutative ring of characteristic $0$, then its underlying chain complex is cofibrant

The category of complexes over a dg-algebra is Grothendieck (it has a generator)

Lifting commutative diagrams of functors from the homotopy level to the "higher" level

Cohomology of derived tensor product of complexes and Künneth spectral sequence

When does the canonical model structure on $\mathcal V$-$\mathbf{Cat}$ give a structure of monoidal model category?

(Homotopy) limits and colimits in a dg-category

The definition of flat sheaves of rings on algebraic stacks

Natural transformations of $A_\infty$-functors (between dg-categories) are "directed homotopies" (reference?)

Can cofibrant replacements of k-linear categories in dg-cat be found k-linear?

When is a triangulated category uniquely determined by its generators?

Universal property of gluing [collage, cograph] of dg-categories

Taking zeroth cohomology of a dg-module over a dg-category is "good" on representables, but probably "bad" on cones

Reconstructing a morphism of exact triangles in the homotopy cat. of a dg-cat. using a "functorial cone map"

Coverings of (DM) stacks and categories of descent data

Morphisms $P \to M$ in the derived category of a dg-category, if $P$ is h-projective

Comparing the definitions of perfect complexes on algebraic stacks and schemes

K-injective (also known as hoinjective) complexes of sheaves of modules

The derived pushforward between derived categories of twisted sheaves preserves (possibly infinite) direct sums

Comparing right and left quasi-representable bimodules

if $I$ is finitely presented nilpotent and $M/IM$ is finitely presented, then $M$ is finitely presented