leanprover-community / mathlib

Lean 3's obsolete mathematical components library: please use mathlib4
https://leanprover-community.github.io/lean3
Apache License 2.0
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[Merged by Bors] - refactor(representation_theory/Rep): define `ihom` concretely #19170

Closed 101damnations closed 1 year ago

101damnations commented 1 year ago

Currently the monoidal closed instance on Rep k G is defined by transporting an instance on a functor category across a category equivalence. This was hard to work with in Lean 3 and is hard to port. This PR defines the monoidal closed instance concretely instead. Naming-wise, the explicit definition of the "internal hom" functor, the right adjoint to left-tensoring, is protected, called Rep.ihom, and then we use that to define a monoidal_closed instance, and then provide a lemma saying the resulting category_theory.ihom is Rep.ihom. Not sure this is the right approach.

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joelriou commented 1 year ago

It looks good to me!

semorrison commented 1 year ago

Me too!

bors merge

bors[bot] commented 1 year ago

Pull request successfully merged into master.

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