proj — Mathlib

English

Projections from a family of modules form a coherent system with Pi, yielding canonical identifications.

Русский

Проекции из семейства модулей образуют когерентную систему с Pi, образуя канонические соответствия.

LaTeX

$$proj and pi coherence$$

Lean4

/-- The projections from a family of modules are linear maps.

Note: this definition would be called `Pi.evalLinearMap` if we followed the pattern established by
`Pi.evalAddHom`, `Pi.evalMonoidHom`, `Pi.evalRingHom`, ... -/
def proj (i : ι) : ((i : ι) → φ i) →ₗ[R] φ i
    where
  toFun := Function.eval i
  map_add' _ _ := rfl
  map_smul' _ _ := rfl

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