Alphabeta MathCoalgebras, Counits, and the Fundamental Coalgebra Theorem
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1 · Prerequisites
Abstract Algebra
- Binary Operations, Monoids, Groups and Subgroups
- Chain Conditions, Semisimple Modules and the Wedderburn–Artin Theorem
- Cosets, Index and Lagrange's Theorem
- Free Modules, Exact Sequences, Projective and Injective Modules
- Group Homomorphisms and the Isomorphism Theorems
- Modules, Submodules, Quotient Modules and the Isomorphism Theorems
- Normal Subgroups and Quotient Groups
- Rings, Subrings, Integral Domains and Fields
- Tensor Products of Modules
Categorification and Geometric Representation Theory
Linear Algebra
Real Analysis
2 · Logical flowchart
3 · Items
Definition
Coalgebra and coalgebra map over a field
Lemma
A finite spanning list contains a basis, without choice
Lemma
Counit uniqueness and finite Sweedler calculus
Definition
Subcoalgebras, coideals, and quotient coalgebras
Lemma
Finite comatrix coalgebras exist
Definition
Group-like elements and primitives relative to a group-like element
Theorem
Coideal quotients, coalgebra-map kernels, and sums of subcoalgebras
Theorem