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Question on why the isomorphism $A \cong \mathbf{Z}^n \oplus \text{Tor} A$ is not natural -- A clarification of Riehl's choice of group?

score 69 · Answer 1 · 2026-05-11 08:40:55

Question on why the isomorphism $A \cong \mathbf{Z}^n \oplus \text{Tor} A$ is not natural -- A clarification of Riehl's choice of group?

score 290 · Answer 2 · 2026-04-28 08:36:11

290

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Does the direct sum have a universal property in the category of groups?

Published on 28 Apr 2026 - 8:36

score 57 · Answer 3 · 2026-04-15 21:22:57

57

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Generalizing Adamek's categories of $T$-spaces

Published on 15 Apr 2026 - 21:22

score 86 · Answer 4 · 2026-05-11 03:57:00

86

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Stack comparison lemma

Published on 11 May 2026 - 3:57

score 46 · Answer 5 · 2026-04-15 11:17:33

46

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Borceux vs. Adamek - Topological Functors

Published on 15 Apr 2026 - 11:17

score 79 · Answer 6 · 2026-04-15 05:47:15

What are the free categories generated from a graph with a single object and no edge and a single object with one directed edge?

score 38 · Answer 7 · 2026-05-10 20:26:46

38

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Why do we have $s.\chi_x=\chi_x$ implies that $s(x)=x u$ for some $u \in \mathfrak{C}^{*, 0}$ in an inverse semigroup?

Published on 10 May 2026 - 20:26

score 75 · Answer 8 · 2026-04-16 03:23:15

75

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A category is filtered if and only if every finite diagram has a cocone

Published on 16 Apr 2026 - 3:23

score 69 · Answer 9 · 2026-04-17 15:30:43

69

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Why is $G \lim F \to \lim (G \circ F)$ natural in $F$?

Published on 17 Apr 2026 - 15:30

score 118 · Answer 10 · 2026-04-15 12:38:28

118

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Left adjoint of forgetful functor $\mathbf{Field}\to\mathbf{Set}$

Published on 15 Apr 2026 - 12:38

score 83 · Answer 11 · 2026-03-29 08:56:02

83

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Natural transformation between functors induces homotopy between maps on the nerve

Published on 29 Mar 2026 - 8:56

score 58 · Answer 12 · 2026-04-09 17:35:03

58

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Are Epi-Mono factorization systems actually Epi-ExtremalMono factorization systems?

Published on 09 Apr 2026 - 17:35

score 50 · Answer 13 · 2026-04-13 00:26:01

50

Views

Proof that a certain morphism doesn't depend on the lift chosen initially

Published on 13 Apr 2026 - 0:26

score 53 · Answer 14 · 2026-04-13 22:47:53

53

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How do I define a notion of infinite coproducts for objects in a category?

Published on 13 Apr 2026 - 22:47

score 51 · Answer 15 · 2026-04-16 00:55:56

51

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Reconstructing isomorphisms via the bijection between the corresponding posets of subobjects

Published on 16 Apr 2026 - 0:55

List Question

Question on why the isomorphism $A \cong \mathbf{Z}^n \oplus \text{Tor} A$ is not natural -- A clarification of Riehl's choice of group?

Does the direct sum have a universal property in the category of groups?

Generalizing Adamek's categories of $T$-spaces

Stack comparison lemma

Borceux vs. Adamek - Topological Functors

What are the free categories generated from a graph with a single object and no edge and a single object with one directed edge?

Why do we have $s.\chi_x=\chi_x$ implies that $s(x)=x u$ for some $u \in \mathfrak{C}^{*, 0}$ in an inverse semigroup?

A category is filtered if and only if every finite diagram has a cocone

Why is $G \lim F \to \lim (G \circ F)$ natural in $F$?

Left adjoint of forgetful functor $\mathbf{Field}\to\mathbf{Set}$

Natural transformation between functors induces homotopy between maps on the nerve

Are Epi-Mono factorization systems actually Epi-ExtremalMono factorization systems?

Proof that a certain morphism doesn't depend on the lift chosen initially

How do I define a notion of infinite coproducts for objects in a category?

Reconstructing isomorphisms via the bijection between the corresponding posets of subobjects

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