The Clowder Project

A

• Akiva Weinberger, Is composition of two transitive relations transitive? If not, can you give me a counterexample?
• Albert Verbeek, Homogeneity of the Hilbert Cube: Notes Taken by A. Verbeek From Lectures by J. de Groot
• Alex Ravsky, Product (arbitrary) of open functions is open.
• AlmostTrivial, The Hilbert Cube in the Product Topology and Box Topology
• André Belotto, Notes About Dedekind Cuts
• Anna Beliakova, Zaur Guliyev, Kazuo Habiro and Aaron D. Lauda, Trace as an Alternative Decategorification Functor
• Aristide Deleanu, Armin Frei and Peter Hilton, Idempotent Triples and Completion

B

• Benjamin Steinberg, Representation Theory of Finite Groups
• Brian M. Scott, Finite Product of Closed Maps Need Not Be Closed

C

• Czesław Bessaga and Aleksander Pełczyński, Selected Topics in Infinite-Dimensional Topology

D

• Daniel Fischer, Proving the derived set $E'$ is closed.
• David Gepner, Moritz Groth and Thomas Nikolaus, Universality of Multiplicative Infinite Loop Space Machines

E

• Emily, Existence of a *really* nice topology on the powerset of a topological space
• Emily de Oliveira Santos, Characterisations of functors $F$ such that $F^*$ or $F_*$ is [property], e.g. faithful, conservative, etc
• Emily de Oliveira Santos, Existence and characterisations of left Kan extensions and liftings in the bicategory of relations I
• Emily de Oliveira Santos, Existence and characterisations of left Kan extensions and liftings in the bicategory of relations II
• Emily de Oliveira Santos, Is a pseudomonic and pseudoepic functor necessarily an equivalence of categories?
• Emily de Oliveira Santos, Looking for a nice characterisation of functors $F$ whose precomposition functor $F^*$ is full
• Emily de Oliveira Santos, What are the 2-categorical mono/epimorphisms in the 2-category of relations?
• Emily Riehl, Category Theory in Context
• Erwin Klein and Anthony C. Thompson, Theory of Correspondences

F

• Fosco Loregian, (Co)end Calculus
• Francis Borceux, Handbook of Categorical Algebra I

G

• Georges Elencwajg, Are all connected manifolds homogeneous?
• Giorgio Mossa, Natural transformations as categorical homotopies

H

• H. H. Schaefer and M. P. Wolff, Topological Vector Spaces

I

• Ittay Weiss, The Reals as Rational Cauchy Filters
• 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.
• J. van Mill, Infinite-Dimensional Topology
• James R. Munkres, Topology
• Jason DeVito, Why is the Hilbert Cube homogeneous?
• Jiří Adámek, Robert El Bashir, Manuela Sobral and Jiří Velebil, On Functors Which Are Lax Epimorphisms
• JMoravitz, Prove if two relations are antisymmetric then their composition is also antisymmetric
• 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
• João Araújo, Michael Kinyon, Janusz Konieczny and António Malheiro, Four Notions of Conjugacy for Abstract Semigroups

K

• Kevin A. Broughan, Adic Topologies for the Rational Integers
• kilian, Equivalence of categories and axiom of choice
• Krzysztof Ciesielski, Set Theory for the Working Mathematician

M

• M. Denise Halverson and David G. Wright, The Homogeneous Property of the Hilbert Cube
• Martin Brandenburg, Why are the category of pointed sets and the category of sets and partial functions “essentially the same”?
• Maximilien Péroux and Brooke Shipley, Coalgebras in Symmetric Monoidal Categories of Spectra

N

• Naïm Camille Favier, PostcomposeNotFull
• Neil Strickland, Proof that a cartesian category is monoidal
• Nelson Martins-Ferreira and Manuela Sobral, Schreier Split Extensions of Preordered Monoids
• Nicolas Bourbaki, General Topology. Chapters 1–4
• Niles Johnson and Donald Yau, 2-Dimensional Categories
• nLab Authors, Boundary
• nLab Authors, Bump Function
• nLab Authors, Displayed Category
• nLab Authors, Groupoid
• nLab Authors, Skeleton
• Noam Zeilberger, Functors in Isbell duality exchange $f^{*}a$ and $f_{*}a$

P

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

Q

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

R

• R. D. Arthan, The Eudoxus Real Numbers
• Robert E. Megginson, An Introduction to Banach Space Theory

S

• 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
• Todd Kemp, Cauchy's Construction of ℝ

U

• user30818, Category and the axiom of choice

V

• Victor, Pushout in the category of sets: proof
• Vinny Chase, $P(X)$ with symmetric difference as addition as a vector space over $\mathbb {Z}_2$

W

• Wikipedia Contributors, James's Space — Wikipedia, The Free Encyclopedia
• Wikipedia Contributors, Multivalued Function — Wikipedia, The Free Encyclopedia
• Wikipedia Contributors, Representation Theory of Finite Groups — Wikipedia, The Free Encyclopedia
• Wikipedia Contributors, Symmetric Difference — Wikipedia, The Free Encyclopedia

Z

• 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