User Peter LeFanu Lumsdaine

10 votes

Why in Martin-Löf type theory any natural number is assumed to be either $0$ or $S(a)$ for some $a\in\mathsf{N}$?

answered Jan 11, 2022 at 10:33

10 votes

Why are the source-target rules of composition always strictly defined?

answered Oct 15, 2023 at 14:25

9 votes

Accepted

Can we always make a strictly functorial choice of pullbacks/re-indexing?

answered Aug 30, 2017 at 20:34

9 votes

What's the point of "created limits"?

answered Sep 20, 2018 at 10:01

9 votes

Accepted

Two monoidal structures and copowering

answered Mar 27, 2019 at 20:59

9 votes

Accepted

Axiom of Replacement in Category Theory

answered Oct 5, 2010 at 19:54

9 votes

Non-examples of model structures, that fail for subtle/surprising reasons?

answered May 7, 2010 at 3:36

9 votes

Accepted

Two pullback diagram

answered Sep 25, 2013 at 15:59

8 votes

What is an intuitive view of adjoints? (version 1: category theory)

answered Dec 4, 2009 at 21:48

8 votes

When is it okay to intersect infinite families of proper classes?

answered Jan 31, 2019 at 13:51

8 votes

Accepted

Is there a constructive proof that in four dimensions, the PL and the smooth category are equivalent?

answered Jan 6, 2019 at 14:52

8 votes

Accepted

How is the morphism of composition in the enriched category of modules constructed?

answered Sep 19, 2021 at 10:05

8 votes

Accepted

Pullback and pseudoelements

answered Apr 8, 2022 at 16:52

8 votes

Most general context where a "disjoint sum" definition of a direct limit is applicable and always exist

answered Oct 9, 2019 at 8:18

8 votes

Accepted

In what sense does the sentence $\operatorname{con}(\mathsf{PA})$ "say" that $\mathsf{PA}$ is consistent?

answered Nov 24, 2023 at 17:33

8 votes

Accepted

Is the Rado graph the unique countable graph that has all finite graphs as induced subgraphs?

answered Nov 29, 2023 at 14:01

8 votes

Accepted

Epimorphisms of relations

answered Sep 25, 2023 at 16:02

7 votes

Accepted

Consistency in pure type systems

answered Sep 10, 2023 at 14:11

7 votes

An application of ping-pong lemma

answered May 16, 2023 at 14:16

7 votes

Can we write Tangled Type Theory without reference to type sequences?

answered Jul 27, 2022 at 10:34

7 votes

Accepted

Is the category of modules over a commutative ring the category of abelian objects in a topos?

answered Feb 4, 2023 at 16:31

7 votes

Books containing new results

answered Feb 5, 2023 at 21:34

7 votes

Adjusting the definition of a well-powered category to category theory with universes: size issues

answered Oct 21, 2019 at 17:59

7 votes

Accepted

Possible to prove a lemma from Godel's completeness theorem in intuitionistic logic?

answered Sep 30, 2019 at 15:25

7 votes

Multiplication and division by a morphism under the “inner composition” in closed monoidal categories

answered Jun 30, 2019 at 12:08

7 votes

Accepted

Dehornoy's proof that the application of two elementary embeddings is an elementary embedding

answered Dec 22, 2021 at 13:12

7 votes

Accepted

Map from the Multiset Monad to the Giry Monad: From Data to Probabilities

answered Sep 18, 2018 at 22:15

7 votes

Accepted

Does Regularity schema imply $\in$-induction when added to first order Zermelo set theory?

answered Nov 7, 2018 at 21:41

7 votes

$\mathscr{U}$-categories and $\mathsf{Hom}$-functors

answered Nov 23, 2018 at 23:01

7 votes

Upgrade adjunction to equivalence

answered Dec 7, 2018 at 18:23

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175 Answers

Why in Martin-Löf type theory any natural number is assumed to be either $0$ or $S(a)$ for some $a\in\mathsf{N}$?

Why are the source-target rules of composition always strictly defined?

Can we always make a strictly functorial choice of pullbacks/re-indexing?

What's the point of "created limits"?

Two monoidal structures and copowering

Axiom of Replacement in Category Theory

Non-examples of model structures, that fail for subtle/surprising reasons?

Two pullback diagram

What is an intuitive view of adjoints? (version 1: category theory)

When is it okay to intersect infinite families of proper classes?

Is there a constructive proof that in four dimensions, the PL and the smooth category are equivalent?

How is the morphism of composition in the enriched category of modules constructed?

Pullback and pseudoelements

Most general context where a "disjoint sum" definition of a direct limit is applicable and always exist

In what sense does the sentence $\operatorname{con}(\mathsf{PA})$ "say" that $\mathsf{PA}$ is consistent?

Is the Rado graph the unique countable graph that has all finite graphs as induced subgraphs?

Epimorphisms of relations

Consistency in pure type systems

An application of ping-pong lemma

Can we write Tangled Type Theory without reference to type sequences?

Is the category of modules over a commutative ring the category of abelian objects in a topos?

Books containing new results

Adjusting the definition of a well-powered category to category theory with universes: size issues

Possible to prove a lemma from Godel's completeness theorem in intuitionistic logic?

Multiplication and division by a morphism under the “inner composition” in closed monoidal categories

Dehornoy's proof that the application of two elementary embeddings is an elementary embedding

Map from the Multiset Monad to the Giry Monad: From Data to Probabilities

Does Regularity schema imply $\in$-induction when added to first order Zermelo set theory?

$\mathscr{U}$-categories and $\mathsf{Hom}$-functors

Upgrade adjunction to equivalence