The Clowder Project

A

• •Akiva Weinberger, Is composition of two transitive relations transitive? If not, can you give me a counterexample?
• •Aristide Deleanu, Armin Frei and Peter Hilton, Idempotent Triples and Completion

D

• •David Gepner, Moritz Groth and Thomas Nikolaus, Universality of Multiplicative Infinite Loop Space Machines

E

• •Eduardo Dubuc and Ross Street, Dinatural Transformations
• •Emily, Gaps in the category theory literature you'd like to see filled
• •Emily, Is a pseudomonic and pseudoepic functor necessarily an equivalence of categories?
• •Emily, Characterisations of functors $F$ such that $F^*$ or $F_*$ is [property], e.g. faithful, conservative, etc
• •Emily, Looking for a nice characterisation of functors $F$ whose precomposition functor $F^*$ is full
• •Emily, Existence and characterisations of left Kan extensions and liftings in the bicategory of relations II
• •Emily, Existence and characterisations of left Kan extensions and liftings in the bicategory of relations I
• •Emily, What are the 2-categorical mono/epimorphisms in the 2-category of relations?
• •Emily Riehl, Category Theory in Context

F

• •Fosco, Answer to “Gaps in the category theory literature you'd like to see filled”
• •Francis Borceux, Handbook of Categorical Algebra I

G

• •Giorgio Mossa, Natural transformations as categorical homotopies

I

• •Ivan Di Liberti, Characterization of pseudo monomorphisms and pseudo epimorphisms in Cat

J

• •J. B., Show that the powerset partial order is a cartesian closed category
• •Jacob Lurie, Kerodon
• •Jiří Adámek, Robert El Bashir, Manuela Sobral and Jiří Velebil, On Functors Which Are Lax Epimorphisms
• •John C. Baez and Michael Shulman, Lectures on $n$-Categories and Cohomology
• •John R. Isbell, Epimorphisms and Dominions. III
• •Jonas Frey, On the 2-Categorical Duals of (Full and) Faithful Functors

K

• •kilian, Equivalence of categories and axiom of choice
• •Krzysztof Ciesielski, Set Theory for the Working Mathematician

M

• •Martin Brandenburg, Why are the category of pointed sets and the category of sets and partial functions “essentially the same”?
• •Maxime Ramzi, Answer to “What theorems or insights are well known for ∞-categories but not well known for categories?”
• •Maximilien Péroux and Brooke Shipley, Coalgebras in Symmetric Monoidal Categories of Spectra

N

• •Neil Strickland, Proof that a cartesian category is monoidal
• •Nick Gurski, Niles Johnson and Angélica M. Osorno, The Symmetric Monoidal 2-Category of Permutative Categories
• •Nick Hu, Answer to “Gaps in the category theory literature you'd like to see filled”
• •Niles Johnson and Donald Yau, 2-Dimensional Categories
• •nLab Authors, Groupoid
• •nLab Authors, Interactions of Images and Pre-images with Unions and Intersections
• •nLab Authors, Displayed Category
• •nLab Authors, Skeleton
• •Noah Snyder, Answer to “Gaps in the category theory literature you'd like to see filled”

P

• •Peter LeFanu Lumsdaine, Epimorphisms of relations
• •Proof Wiki Contributors, Preimage of Intersection Under Mapping — Proof Wiki
• •Proof Wiki Contributors, Preimage of Union Under Mapping — Proof Wiki
• •Proof Wiki Contributors, Image of Intersection Under Mapping — Proof Wiki
• •Proof Wiki Contributors, Image of Union Under Mapping — Proof Wiki
• •Proof Wiki Contributors, Characteristic Function of Union — Proof Wiki
• •Proof Wiki Contributors, Characteristic Function of Intersection — Proof Wiki
• •Proof Wiki Contributors, Characteristic Function of Set Difference — Proof Wiki
• •Proof Wiki Contributors, Union of Symmetric Differences — Proof Wiki
• •Proof Wiki Contributors, Symmetric Difference on Power Set Forms Abelian Group — Proof Wiki
• •Proof Wiki Contributors, Characteristic Function of Symmetric Difference — Proof Wiki
• •Proof Wiki Contributors, Symmetric Difference of Complements — Proof Wiki
• •Proof Wiki Contributors, Intersection Distributes Over Symmetric Difference — Proof Wiki
• •Proof Wiki Contributors, Symmetric Difference With Universe — Proof Wiki
• •Proof Wiki Contributors, Symmetric Difference With Complement — Proof Wiki
• •Proof Wiki Contributors, Symmetric Difference With Self Is Empty Set — Proof Wiki
• •Proof Wiki Contributors, Symmetric Difference With Empty Set — Proof Wiki
• •Proof Wiki Contributors, Symmetric Difference Is Commutative — Proof Wiki
• •Proof Wiki Contributors, Symmetric Difference Is Associative — Proof Wiki
• •Proof Wiki Contributors, Equivalence of Definitions of Symmetric Difference — Proof Wiki
• •Proof Wiki Contributors, Set Difference With Empty Set Is Self — Proof Wiki
• •Proof Wiki Contributors, Set Difference With Self Is Empty Set — Proof Wiki
• •Proof Wiki Contributors, Set Difference as Symmetric Difference With Intersection — Proof Wiki
• •Proof Wiki Contributors, Set Difference With Subset Is Superset of Set Difference — Proof Wiki
• •Proof Wiki Contributors, Intersection With Set Difference Is Set Difference With Intersection — Proof Wiki
• •Proof Wiki Contributors, Set Difference With Set Difference Is Union of Set Difference With Intersection — Proof Wiki
• •Proof Wiki Contributors, Set Difference as Intersection With Complement — Proof Wiki
• •Proof Wiki Contributors, Cartesian Product Is Empty Iff Factor Is Empty — Proof Wiki
• •Proof Wiki Contributors, Bijection Between $S\times T$ and $T\times S$ — Proof Wiki
• •Proof Wiki Contributors, Bijection Between $R\times (S\times T)$ and $(R\times S)\times T$ — Proof Wiki
• •Proof Wiki Contributors, Complement of Complement — Proof Wiki
• •Proof Wiki Contributors, Set Difference With Union — Proof Wiki
• •Proof Wiki Contributors, Set Difference Is Right Distributive Over Union — Proof Wiki
• •Proof Wiki Contributors, De Morgan's Laws (Set Theory)/Set Difference/Difference with Union — Proof Wiki
• •Proof Wiki Contributors, De Morgan's Laws (Set Theory) — Proof Wiki
• •Proof Wiki Contributors, Set Difference Over Subset — Proof Wiki
• •Proof Wiki Contributors, Complement of Preimage equals Preimage of Complement — Proof Wiki
• •Proof Wiki Contributors, Preimage of Set Difference Under Mapping — Proof Wiki
• •Proof Wiki Contributors, Image of Set Difference Under Mapping — Proof Wiki
• •Proof Wiki Contributors, Intersection With Subset Is Subset — Proof Wiki
• •Proof Wiki Contributors, Set Intersection Distributes Over Union — Proof Wiki
• •Proof Wiki Contributors, Set Intersection Is Idempotent — Proof Wiki
• •Proof Wiki Contributors, Intersection With Empty Set — Proof Wiki
• •Proof Wiki Contributors, Intersection Is Commutative — Proof Wiki
• •Proof Wiki Contributors, Intersection Is Associative — Proof Wiki
• •Proof Wiki Contributors, Set Intersection Preserves Subsets — Proof Wiki
• •Proof Wiki Contributors, Union Distributes Over Intersection — Proof Wiki
• •Proof Wiki Contributors, Set Union Is Idempotent — Proof Wiki
• •Proof Wiki Contributors, Union as Symmetric Difference With Intersection — Proof Wiki
• •Proof Wiki Contributors, Set Union Preserves Subsets — Proof Wiki
• •Proof Wiki Contributors, Union With Empty Set — Proof Wiki
• •Proof Wiki Contributors, Union Is Associative — Proof Wiki
• •Proof Wiki Contributors, Union Is Commutative — Proof Wiki
• •Proof Wiki Contributors, Quotient Mapping Is Coequalizer — Proof Wiki
• •Proof Wiki Contributors, Cartesian Product of Intersections — Proof Wiki
• •Proof Wiki Contributors, Cartesian Product Distributes Over Union — Proof Wiki
• •Proof Wiki Contributors, Cartesian Product Distributes Over Set Difference — Proof Wiki
• •Proof Wiki Contributors, Cartesian Product Distributes Over Symmetric Difference — Proof Wiki
• •Proof Wiki Contributors, Condition For Mapping From Quotient Set To Be Well-Defined — Proof Wiki
• •Proof Wiki Contributors, Condition For Mapping From Quotient Set To Be An Injection— Proof Wiki
• •Proof Wiki Contributors, Condition For Mapping from Quotient Set To Be A Surjection — Proof Wiki
• •Proof Wiki Contributors, Mapping From Quotient Set When Defined Is Unique — Proof Wiki
• •Proof Wiki Contributors, Symmetric Difference With Intersection Forms Ring — Proof Wiki
• •Proof Wiki Contributors, Symmetric Difference With Union Does Not Form Ring — Proof Wiki

Q

• •Qiaochu Yuan, Is the category of pointed sets Cartesian closed?
• •Qiaochu Yuan, Mono's and epi's in the category Rel?

S

• •Saunders Mac Lane, Categories for the Working Mathematician
• •Stefan Hamcke, Precomposition with a faithful functor
• •Stephen Schanuel and Ross Street, The Free Adjunction
• •Susan Niefield, Change of Base for Relational Variable Sets

T

• •Theo Johnson-Freyd and Claudia Scheimbauer, (Op)lax Natural Transformations, Twisted Quantum Field Theories, and “Even Higher” Morita Categories
• •Tim Campion, Answer to “Existence and characterisations of left Kan extensions and liftings in the bicategory of relations I”

V

• •Victor, Pushout in the category of sets: proof
• •Vinny Chase, $\mathcal {P}(X)$ with symmetric difference as addition as a vector space over $\mathbb {Z}_{2}$

W

• •Wikipedia Contributors, Symmetric Difference — Wikipedia, The Free Encyclopedia
• •Wikipedia Contributors, Multivalued Function — Wikipedia, The Free Encyclopedia

Z

• •Zhen Lin, Reference for Basic Multicategory Theory
• •Zhen Lin, Answer to “Category and the axiom of choice”
• •Zhen Lin, If the functor on presheaf categories given by precomposition by F is ff, is F full? faithful?
• •Zhen Lin, Precomposition with a faithful functor
• •Zhen Lin, Show that the powerset partial order is a cartesian closed category.
• •Zhen Lin Low, Notes on Homotopical Algebra