User goblin GONE

49 votes

9 answers

6k views

What recent programmes to alter highly-entrenched mathematical terminology have succeeded, and under what conditions do they tend to succeed or fail?

asked Jul 11, 2014 at 8:38

21 votes

3 answers

2k views

Why would the category of sets be intuitionistic?

set-theory mathematical-philosophy foundations type-theory intuitionism

asked Dec 5, 2016 at 16:54

18 votes

1 answer

2k views

Has anything ever been done with the set $\{1,2,3,4,\ldots\}$ equipped with the operation $a \oplus b = a+b-1$ and the usual notion of multiplication?

nt.number-theory reference-request ac.commutative-algebra ra.rings-and-algebras

asked Feb 14, 2016 at 11:15

13 votes

4 answers

818 views

The groupoid of algebraic expressions and proofs

reference-request lo.logic universal-algebra groupoids homotopy-type-theory

asked Feb 13, 2015 at 15:04

12 votes

7 answers

1k views

Properties of rings that have an elegant description in terms of the associated category of modules

ra.rings-and-algebras big-list modules ac.commutative-algebra

asked Mar 25, 2014 at 9:10

11 votes

4 answers

731 views

What are "nearly initial" objects really called?

ct.category-theory terminology galois-theory

asked Dec 4, 2016 at 14:14

10 votes

1 answer

588 views

Topology from the viewpoint of the filter endofunctor

reference-request ct.category-theory gn.general-topology

asked Mar 26, 2017 at 14:06

10 votes

1 answer

409 views

Does every Lawvere theory arise in this way?

ct.category-theory universal-algebra

asked Jul 28, 2015 at 2:28

9 votes

2 answers

1k views

Is there a "large powerset axiom" so extreme that it disproves the existence of strongly inaccessible cardinals?

set-theory

asked May 22, 2014 at 13:50

9 votes

2 answers

452 views

Is there a notion of "space" such that vector bundles can be understood in this way?

ct.category-theory gn.general-topology differential-topology vector-bundles

asked Apr 30, 2017 at 7:15

8 votes

1 answer

248 views

Is there a version of the "infinitary" disjunctive normal form theorem for topoi and slice categories?

ct.category-theory lo.logic topos-theory

asked Nov 15, 2018 at 9:18

8 votes

0 answers

803 views

Would Ultimate L really "[reduce] all questions of set theory to axioms of strong infinity"?

set-theory

asked Apr 30, 2019 at 4:57

8 votes

0 answers

161 views

Does the "coproduct-elimination transform" have an accepted name, and where can I learn more about it?

ct.category-theory soft-question terminology computer-science type-theory

asked Jul 25, 2020 at 1:58

8 votes

3 answers

1k views

Why isn't there more interest in "large powerset axioms"?

set-theory soft-question

asked Apr 28, 2014 at 20:51

7 votes

2 answers

760 views

Which linearly ordered sets have the property that their completion is equipotent with their powerset?

set-theory order-theory linear-orders

asked Mar 31, 2014 at 7:04

7 votes

1 answer

365 views

Does the forgetful functor $\mathbf{Comp} \rightarrow \mathbf{Top}$ have a left-adjoint?

ct.category-theory gn.general-topology

asked Jul 10, 2017 at 17:59

7 votes

2 answers

902 views

What's the point of "created limits"?

ct.category-theory

asked Sep 20, 2018 at 4:26

7 votes

1 answer

471 views

How (if at all) does category theory deal with situations where the usual notion of isomorphism isn't right?

ct.category-theory

asked Sep 29, 2015 at 9:01

6 votes

2 answers

400 views

For which cardinal numbers $\kappa$ is it consistent with ZFC that $\kappa^{\mathrm{cf}(\kappa)} < \kappa^\kappa$?

set-theory cardinal-arithmetic

asked May 2, 2014 at 5:01

6 votes

1 answer

348 views

Can we have more malleable proper classes without sacrificing conservativity?

set-theory

asked Apr 26, 2014 at 19:56

5 votes

1 answer

408 views

In search of a set theory with specific properties

set-theory new-foundations

asked Sep 1, 2012 at 13:30

5 votes

0 answers

123 views

Question about the poset of inner models

set-theory

asked Jun 3, 2014 at 11:35

5 votes

1 answer

377 views

Is there a large-cardinal completeness theorem for $L$?

set-theory large-cardinals

asked Jun 3, 2014 at 15:43

5 votes

0 answers

131 views

What terminology surrounds "involutive" double categories?

higher-category-theory terminology

asked Feb 27, 2016 at 13:30

5 votes

1 answer

380 views

What do we call this quantifier ("binder")?

lo.logic computer-science foundations formal-languages type-theory

asked Jun 22, 2016 at 17:55

5 votes

1 answer

219 views

Partial $\mathsf{T}$-algebras, where $\mathsf{T}$ is a Lawvere theory

reference-request ct.category-theory universal-algebra

asked Aug 25, 2016 at 17:30

5 votes

0 answers

206 views

Are any formal systems based upon the idea of "iterated characterization pushing" currently in existence? If not, is anyone working on them?

higher-category-theory foundations type-theory axioms

asked Oct 27, 2019 at 5:09

4 votes

0 answers

124 views

Is there any accepted single-word that means "partial function"?

fa.functional-analysis terminology computer-science

asked Mar 8, 2017 at 15:33

4 votes

2 answers

473 views

Is it consistent with ZFC that $\mathrm{dv}(\kappa) = \kappa$ for all infinite cardinal numbers $\kappa$?

set-theory linear-orders

asked May 13, 2014 at 6:41

4 votes

2 answers

368 views

Has this construction, which builds a symmetric multicategory from a commutative monoid, been described or studied anywhere, and if so, where?

reference-request ct.category-theory terminology operads

asked Jan 15, 2015 at 16:57

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66 Questions

What recent programmes to alter highly-entrenched mathematical terminology have succeeded, and under what conditions do they tend to succeed or fail?

Why would the category of sets be intuitionistic?

Has anything ever been done with the set $\{1,2,3,4,\ldots\}$ equipped with the operation $a \oplus b = a+b-1$ and the usual notion of multiplication?

The groupoid of algebraic expressions and proofs

Properties of rings that have an elegant description in terms of the associated category of modules

What are "nearly initial" objects really called?

Topology from the viewpoint of the filter endofunctor

Does every Lawvere theory arise in this way?

Is there a "large powerset axiom" so extreme that it disproves the existence of strongly inaccessible cardinals?

Is there a notion of "space" such that vector bundles can be understood in this way?

Is there a version of the "infinitary" disjunctive normal form theorem for topoi and slice categories?

Would Ultimate L really "[reduce] all questions of set theory to axioms of strong infinity"?

Does the "coproduct-elimination transform" have an accepted name, and where can I learn more about it?

Why isn't there more interest in "large powerset axioms"?

Which linearly ordered sets have the property that their completion is equipotent with their powerset?

Does the forgetful functor $\mathbf{Comp} \rightarrow \mathbf{Top}$ have a left-adjoint?

What's the point of "created limits"?

How (if at all) does category theory deal with situations where the usual notion of isomorphism isn't right?

For which cardinal numbers $\kappa$ is it consistent with ZFC that $\kappa^{\mathrm{cf}(\kappa)} < \kappa^\kappa$?

Can we have more malleable proper classes without sacrificing conservativity?

In search of a set theory with specific properties

Question about the poset of inner models

Is there a large-cardinal completeness theorem for $L$?

What terminology surrounds "involutive" double categories?

What do we call this quantifier ("binder")?

Partial $\mathsf{T}$-algebras, where $\mathsf{T}$ is a Lawvere theory

Are any formal systems based upon the idea of "iterated characterization pushing" currently in existence? If not, is anyone working on them?

Is there any accepted single-word that means "partial function"?

Is it consistent with ZFC that $\mathrm{dv}(\kappa) = \kappa$ for all infinite cardinal numbers $\kappa$?

Has this construction, which builds a symmetric multicategory from a commutative monoid, been described or studied anywhere, and if so, where?