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25 votes

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Jon Beck's untitled manuscript containing the "tripleability theorem" (i.e. the monadicity theorem)

answered Sep 16, 2021 at 18:04

23 votes

Two interpretations of implication in categorical logic?

answered Dec 4, 2020 at 10:39

20 votes

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Is Freyd's thesis available online anywhere?

answered Feb 22 at 18:16

14 votes

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The category theoretic origin of arithmetic product

answered Dec 30, 2023 at 0:26

14 votes

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Strict toposes as a finite limit theory

answered Jun 10 at 10:56

13 votes

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Free category with product and coproduct

answered May 8, 2020 at 20:35

13 votes

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Original reference for categories of presheaves as free cocompletions of small categories

answered Jul 5, 2021 at 14:36

13 votes

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Overloading of the word "local" in category theory

answered Jan 24, 2023 at 15:45

11 votes

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Reference request for Linton's theorems on equational theories

answered May 10, 2021 at 22:45

11 votes

Is there a tricategory of bicategories and biprofunctors?

answered May 15, 2021 at 0:46

11 votes

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Double category of algebras, lax and colax morphisms of algebras

answered Aug 6 at 19:19

10 votes

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Standard reference for double category theory

answered Aug 22 at 18:17

9 votes

Consequences of imposing conditions on the restricted Yoneda embedding of a functor

answered Apr 11 at 19:18

9 votes

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Eilenberg-Moore category as a 2-dimensional limit

answered Aug 5, 2023 at 12:51

9 votes

A cocomma square from the Kleisli category of a monad

answered Aug 5, 2023 at 22:40

9 votes

Merging single-sorted and multi-sorted theories

answered Oct 28 at 7:39

9 votes

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Injectivity of functors in terms of skeletons?

answered Feb 11, 2021 at 17:59

9 votes

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Who introduced the notion of 2-categories?

answered Jun 2, 2023 at 15:58

8 votes

The canonical category defined by a partially defined category

answered May 19, 2023 at 12:14

8 votes

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Enriched 2-categories

answered Jul 28, 2023 at 16:21

8 votes

J.W. Gray's monumental work notes on the formal theory of internal (2-)categories

answered Oct 4, 2022 at 21:55

8 votes

Are there simple conditions on a category C which guaranty that Ind(C) is a Grothendieck topos?

answered Dec 6, 2021 at 15:24

8 votes

Comparing the existing formulations of universal algebra and their levels of generality

answered Apr 2, 2021 at 18:22

8 votes

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Filtered 2-colimits commute with finite 2-limits

answered Apr 27, 2021 at 10:48

8 votes

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Name for a categorical adjunction that is a "semi-equivalence"

answered Oct 21, 2021 at 15:01

8 votes

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When is the Eilenberg-Moore category of a monad on an ind-category itself an ind-category?

answered Mar 16, 2022 at 16:15

7 votes

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Is $\mathit{Topos}^\text{op} \to \mathit{Pr}^L$ monadic?

answered May 2, 2022 at 21:08

7 votes

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Relative cocompletion of a category

answered May 15, 2021 at 12:19

7 votes

What are "nearly initial" objects really called?

answered Dec 24, 2020 at 13:03

7 votes

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Enriched categories over a semi-monoidal category

answered Sep 14, 2022 at 11:16

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95 Answers

Jon Beck's untitled manuscript containing the "tripleability theorem" (i.e. the monadicity theorem)

Two interpretations of implication in categorical logic?

Is Freyd's thesis available online anywhere?

The category theoretic origin of arithmetic product

Strict toposes as a finite limit theory

Free category with product and coproduct

Original reference for categories of presheaves as free cocompletions of small categories

Overloading of the word "local" in category theory

Reference request for Linton's theorems on equational theories

Is there a tricategory of bicategories and biprofunctors?

Double category of algebras, lax and colax morphisms of algebras

Standard reference for double category theory

Consequences of imposing conditions on the restricted Yoneda embedding of a functor

Eilenberg-Moore category as a 2-dimensional limit

A cocomma square from the Kleisli category of a monad

Merging single-sorted and multi-sorted theories

Injectivity of functors in terms of skeletons?

Who introduced the notion of 2-categories?

The canonical category defined by a partially defined category

Enriched 2-categories

J.W. Gray's monumental work notes on the formal theory of internal (2-)categories

Are there simple conditions on a category C which guaranty that Ind(C) is a Grothendieck topos?

Comparing the existing formulations of universal algebra and their levels of generality

Filtered 2-colimits commute with finite 2-limits

Name for a categorical adjunction that is a "semi-equivalence"

When is the Eilenberg-Moore category of a monad on an ind-category itself an ind-category?

Is $\mathit{Topos}^\text{op} \to \mathit{Pr}^L$ monadic?

Relative cocompletion of a category

What are "nearly initial" objects really called?

Enriched categories over a semi-monoidal category