Welcome to Covariance
The search for the most useful set-theoretical foundations for category theory is a fascinating topic that unfortunately would require too long of a digression to explore. Instead, we sweep these foundational issues under the rug, not because these issues are not serious or interesting, but because they distract from the task at hand.
Recently updated notes
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Scholarships & Awards | 3:37 PM - April 25, 2025 |
Donald and Diana Jackson Scholarship in Honor of Clyde Fisher | 9:48 AM - April 25, 2025 |
Clyde P. Fisher Memorial | 9:43 AM - April 25, 2025 |
Knowledge
Mathematics
Algebra theory
Not to be confused with the general concept of algebra (abstract or otherwise), an algebra is an algebraic structure similar to a module, only with two internal binary operations.
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Algebras | 7:21 AM - March 31, 2025 |
Exterior algebras | 7:22 AM - March 31, 2025 |
Symmetric algebras | 7:23 AM - March 31, 2025 |
Symmetric and alternating tensors | 7:23 AM - March 31, 2025 |
Tensor algebras | 7:23 AM - March 31, 2025 |
Algebraic geometry
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Examples of classical conic duality | 7:24 AM - March 31, 2025 |
Category theory
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Abelian categories | 12:33 PM - March 31, 2025 |
Additive categories | 12:34 PM - March 31, 2025 |
Adjoints | 12:38 PM - March 31, 2025 |
Categories | 12:40 PM - March 31, 2025 |
Chain complexes | 12:34 PM - March 31, 2025 |
Diagram chases without elements | 7:26 PM - November 23, 2024 |
Diagram lemmas | 12:34 PM - March 31, 2025 |
Double complexes and mural maps | 12:35 PM - March 31, 2025 |
Exact sequences and chain homology | 12:35 PM - March 31, 2025 |
Examples of adjoints | 12:39 PM - March 31, 2025 |
Functor categories | 12:46 PM - March 31, 2025 |
Functors | 12:46 PM - March 31, 2025 |
Natural transformations | 12:47 PM - March 31, 2025 |
Preadditive categories | 12:36 PM - March 31, 2025 |
Properties of adjoints | 12:39 PM - March 31, 2025 |
Special morphisms | 12:47 PM - March 31, 2025 |
Spectral sequences | 12:37 PM - March 31, 2025 |
The Salamander Lemma | 12:37 PM - March 31, 2025 |
Universal arrows and elements | 12:48 PM - March 31, 2025 |
Universal Properties I - Inspiring Examples | 12:48 PM - March 31, 2025 |
Universal Properties II - Commutative diagrams, cones and limits | 10:38 AM - April 01, 2025 |
Universal Properties III - Yoneda's Lemma | 12:50 PM - March 31, 2025 |
Field theory
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A question about finite fields | 7:24 AM - March 31, 2025 |
Group theory
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Normal subgroups | 7:25 AM - March 31, 2025 |
Module theory
Representation theory
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Representations of groups | 2:31 PM - April 09, 2025 |
Ring theory
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Chinese Remainder Theorem | 7:25 AM - March 31, 2025 |
Graded rings | 7:25 AM - March 31, 2025 |
Least common multiples | 7:34 PM - July 21, 2024 |
Principal ideal domains (PIDs) | 6:29 AM - May 07, 2024 |
Tropical algebraic geometry
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Investigation into tropical tangency loci | 7:27 AM - March 31, 2025 |
Linear tropical varieties | 7:27 AM - March 31, 2025 |
Quadratic tropical varieties | 7:27 AM - March 31, 2025 |
Tropical varieties | 7:27 AM - March 31, 2025 |
Software
Blender
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Houdini
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Systems of equations | 2:56 PM - August 06, 2024 |