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The FreeCommAlgebra on a coproduct of types #925

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merged 24 commits into from
Sep 14, 2022

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felixwellen
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@felixwellen felixwellen commented Sep 2, 2022

This PR is about proving the relation

R[I ⊎ J] = R[I][J]

where I and J are types which function as index-types for the variables in the generalized polynomial-rings R[I] and R[I][J]. This can be used to show that

R[Fin n][Fin m] = R[Fin (n+m)]

which are the standard multivariate polynomials in n,m and n+m variables. This also works for sets merely equivalent to some Fin k, so a version with actions of permutations can also be defined.
The PR also adds base change for commutative algebras (from R-Algebras to S-Algebras along a hom f:S->R).

@felixwellen felixwellen force-pushed the freeCommAlgebra_comm_coproduct branch 5 times, most recently from 62260e2 to 284e82f Compare September 8, 2022 08:01
@felixwellen felixwellen marked this pull request as ready for review September 12, 2022 07:43
… into freeCommAlgebra_comm_coproduct

# Conflicts:
#	Cubical/Algebra/CommAlgebra/FreeCommAlgebra/OnCoproduct.agda
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@MatthiasHu MatthiasHu left a comment

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Great stuff! :-)
Here are some comments.

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@MatthiasHu MatthiasHu left a comment

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This can be merged now imo!

@felixwellen felixwellen merged commit 1e9ce67 into agda:master Sep 14, 2022
@felixwellen felixwellen deleted the freeCommAlgebra_comm_coproduct branch September 14, 2022 14:10
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2 participants