Question

Homotopy invariance of functors

score 129 · Answer 1 · 2023-10-28 16:45:13

129

Views

Homotopy invariance of functors

Published on 28 Oct 2023 - 16:45

score 43 · Answer 2 · 2026-03-25 17:41:55

43

Views

Condition that limit of a diagram $F$ exists if $\alpha: Mor(-,L) \to \lim Mor(X,F(i))$

Published on 25 Mar 2026 - 17:41

score 45 · Answer 3 · 2023-10-30 22:58:43

45

Views

Every object of category $\mathcal{C}$ is compact in $Ind(\mathcal{C})$

Published on 30 Oct 2023 - 22:58

score 30 · Answer 4 · 2026-03-22 05:04:44

30

Views

Convergence of analytic functors?

Published on 22 Mar 2026 - 5:04

score 45 · Answer 5 · 2023-11-02 13:10:29

45

Views

Two isomorphism about restriction function and idempotent embedding functor

Published on 02 Nov 2023 - 13:10

score 52 · Answer 6 · 2023-11-11 17:07:26

52

Views

$F : I → C$ is a functor from a filtered category with any colimit. $ι : J → I$ is the embedding with $J$ cofinal. Then colim $F \cong$ colim($F ◦ ι$)

Published on 11 Nov 2023 - 17:07

score 112 · Answer 7 · 2023-11-12 10:01:07

112

Views

Covariant power object functor?

Published on 12 Nov 2023 - 10:01

score 59 · Answer 8 · 2023-11-13 02:24:48

59

Views

Intersection of vector spaces and inclusion-exclusion

Published on 13 Nov 2023 - 2:24

score 55 · Answer 9 · 2026-03-25 15:42:28

55

Views

Proving the existance and uniqueness of the unit of an adjunction

Published on 25 Mar 2026 - 15:42

score 49 · Answer 10 · 2026-03-26 17:33:17

49

Views

$F : C \to D$ is an equivalence of categories with quasi-inverse $G: D \to C$. Does the pair $(F,G)$ necessarily form an adjunction?

Published on 26 Mar 2026 - 17:33

score 33 · Answer 11 · 2026-03-25 01:36:13

33

Views

Functor $−\otimes_R L$ is right exact

Published on 25 Mar 2026 - 1:36

score 37 · Answer 12 · 2023-11-20 13:03:54

37

Views

The R-module $P$ is projective (the functor Hom$_R(P, −)$ : R-Mod $\to$ Ab is exact) iff the lifting property holds

Published on 20 Nov 2023 - 13:03

score 41 · Answer 13 · 2026-03-26 18:37:16

41

Views

The free 2-category on a 1-category with respect to pseudo-functors into 2-categories

Published on 26 Mar 2026 - 18:37

score 52 · Answer 14 · 2023-11-27 06:45:47

52

Views

$Ext^n(A,B)\cong H^n(Hom(A,I^\bullet)) $, with $I^\bullet$ an injective resolution of B

Published on 27 Nov 2023 - 6:45

score 80 · Answer 15 · 2026-03-22 07:13:06

80

Views

Endomorphisms of an equivalence of categories

Published on 22 Mar 2026 - 7:13

List Question

Homotopy invariance of functors

Condition that limit of a diagram $F$ exists if $\alpha: Mor(-,L) \to \lim Mor(X,F(i))$

Every object of category $\mathcal{C}$ is compact in $Ind(\mathcal{C})$

Convergence of analytic functors?

Two isomorphism about restriction function and idempotent embedding functor

$F : I → C$ is a functor from a filtered category with any colimit. $ι : J → I$ is the embedding with $J$ cofinal. Then colim $F \cong$ colim($F ◦ ι$)

Covariant power object functor?

Intersection of vector spaces and inclusion-exclusion

Proving the existance and uniqueness of the unit of an adjunction

$F : C \to D$ is an equivalence of categories with quasi-inverse $G: D \to C$. Does the pair $(F,G)$ necessarily form an adjunction?

Functor $−\otimes_R L$ is right exact

The R-module $P$ is projective (the functor Hom$_R(P, −)$ : R-Mod $\to$ Ab is exact) iff the lifting property holds

The free 2-category on a 1-category with respect to pseudo-functors into 2-categories

$Ext^n(A,B)\cong H^n(Hom(A,I^\bullet)) $, with $I^\bullet$ an injective resolution of B

Endomorphisms of an equivalence of categories

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