Alphabeta Math

Graded Bimodules and Tensor Functors

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✓ 6 results · all verified · 2 also independently AI-judged
Every result on this page is machine-checked by a proof checker and read in full and owner-audited; the judge is an additional, independent cross-model AI review of the proofs. The 4 not AI-judged were verified by owner audit (typically over a confirmed judge false positive), not failures.
1 · Prerequisites
Abstract Algebra
Category Theory
Combinatorics
Commutative Algebra
Homological Algebra
Real Analysis
Set Theory
2 · Logical flowchart

3 · Items

Definition

Associative graded algebras, bimodules, and internal shifts

Lemma

Graded modules with degree-zero maps form an abelian category

Definition

Graded balanced tensor product and homogeneous Hom

Lemma

Graded associativity, units, and internal-shift tensor isomorphisms

Definition

Finite graded projective modules

Theorem

Finite graded projectives are finite shifted-free summands

Theorem

Bimodule tensor exactness and preservation of finite projectives have separate hypotheses

Theorem

Associative and graded bimodule tensor–Hom adjunction

Proposition

Restriction and extension along a graded algebra map

Sources