Question

In triangulated category, why do we use triangles, but not exact sequences?

score 729 · Answer 1 · 2026-04-15 05:37:07

729

Views

In triangulated category, why do we use triangles, but not exact sequences?

Published on 15 Apr 2026 - 5:37

score 348 · Answer 2 · 2026-04-17 05:32:10

348

Views

Riehl's Category Theory in Context - Exercise 1.5.vii without Axiom of Choice

Published on 17 Apr 2026 - 5:32

score 666 · Answer 3 · 2026-04-14 13:02:35

666

Views

In category theory, why do we define the product by its universal property the way we do?

Published on 14 Apr 2026 - 13:02

score 222 · Answer 4 · 2026-03-25 03:02:02

222

Views

Grothendieck group of equivalent categories

Published on 25 Mar 2026 - 3:02

score 88 · Answer 5 · 2026-03-27 05:34:40

88

Views

Marked simplicial sets is cartesian closed.

Published on 27 Mar 2026 - 5:34

score 96 · Answer 6 · 2026-04-11 14:47:49

96

Views

Is there a difference between a pushout and a copullback?

Published on 11 Apr 2026 - 14:47

score 578 · Answer 7 · 2026-03-26 19:18:52

578

Views

"Recursive types for free!" -- But doesn't this contradict the fact that $\mathbb{N} \notin \mathbf{FinSet}$?

Published on 26 Mar 2026 - 19:18

score 352 · Answer 8 · 2026-03-25 19:25:27

352

Views

Filtered colimit of integral domains is an integral domain

Published on 25 Mar 2026 - 19:25

score 34 · Answer 9 · 2026-04-14 05:32:52

34

Views

What are these constructions similar to a pushout and pullback called?

Published on 14 Apr 2026 - 5:32

score 140 · Answer 10 · 2026-03-27 20:29:22

140

Views

Endomorphisms of a monoidal functor

Published on 27 Mar 2026 - 20:29

score 70 · Answer 11 · 2026-04-10 08:09:27

70

Views

Topology generated by a set function from a topological space.

Published on 10 Apr 2026 - 8:09

score 195 · Answer 12 · 2026-04-16 00:52:36

195

Views

Quasi isomorphisms are weak equivalences for the category of chain complexes

Published on 16 Apr 2026 - 0:52

score 520 · Answer 13 · 2026-04-03 07:17:17

520

Views

Soundness and consistency in type theory

Published on 03 Apr 2026 - 7:17

score 65 · Answer 14 · 2026-04-15 13:00:26

65

Views

When can we guarantee the existence of an object satisfying a given universal property, in purely category-theoretic terms?

Published on 15 Apr 2026 - 13:00

score 200 · Answer 15 · 2026-04-10 18:44:23

200

Views

Type theory with dependent products is locally cartesian closed

Published on 10 Apr 2026 - 18:44

List Question

In triangulated category, why do we use triangles, but not exact sequences?

Riehl's Category Theory in Context - Exercise 1.5.vii without Axiom of Choice

In category theory, why do we define the product by its universal property the way we do?

Grothendieck group of equivalent categories

Marked simplicial sets is cartesian closed.

Is there a difference between a pushout and a copullback?

"Recursive types for free!" -- But doesn't this contradict the fact that $\mathbb{N} \notin \mathbf{FinSet}$?

Filtered colimit of integral domains is an integral domain

What are these constructions similar to a pushout and pullback called?

Endomorphisms of a monoidal functor

Topology generated by a set function from a topological space.

Quasi isomorphisms are weak equivalences for the category of chain complexes

Soundness and consistency in type theory

When can we guarantee the existence of an object satisfying a given universal property, in purely category-theoretic terms?

Type theory with dependent products is locally cartesian closed

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