# Algebra

Anki flash cards loosely based on parts of

*Algebra: Chapter 0*by Paolo Aluffi.- Groups. Some properties of order.
- Groups. Lagrange's theorem.
- Canonical decomposition in the Grp category
- Groups. Kernel.
- Normal subgroup
- Quotient group. From equivalence condition.
- Quotient groups. From Cosets.
- Cosets
- Subgroups. Definition.
- Subgroups. Propositions.
- Group homomorphism
- Group homomorphisms and order
- Group Isomorphism
- Groups. All orders divides order of maximal element
- Isomorphisms of cyclic group products
- The set products satisfy the coproduct property in the Abelian category.
- Category of Groups
- Groups. Group datum.
- Groups. Some properties of order.
- Groups. Order for commutative product.
- Groups. Order.
- Groups. 3 basic lemmas.
- Group. Definition.
- Initial and final objects
- Universal properties. Quotient.
- Monomorphisms and epimorphisms
- Endomorphisms and automorphisms
- Isomorphism
- Slice category
- Category Theory. Essence of associative composition.
- Category. Definition.
- Canonical decomposition
- Identity, inclusion and restriction
- Injectivity and surjectivity
- Equivalence relations

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