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Commit 2021-07-10 20:40 90d8d468

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feat(category_theory/monad): monad forget is monadic (#8161) cc @adamtopaz wip since I need to dualise

Estimated changes

Modified src/algebra/category/Group/Z_Module_equivalence.lean

Modified src/algebraic_topology/simplex_category.lean

Modified src/category_theory/Fintype.lean

Modified src/category_theory/adjunction/lifting.lean

Modified src/category_theory/connected_components.lean

Modified src/category_theory/equivalence.lean

Modified src/category_theory/monad/adjunction.lean

added def category_theory.adjunction.adj_to_comonad_iso

added def category_theory.adjunction.adj_to_monad_iso

modified def category_theory.adjunction.to_comonad

modified def category_theory.adjunction.to_monad

modified def category_theory.comonad.comparison

added def category_theory.comonad.comparison_forget

added theorem category_theory.comonad.left_comparison

deleted def category_theory.comparison_forget

modified def category_theory.monad.comparison

modified def category_theory.monad.comparison_forget

added theorem category_theory.monad.left_comparison

Modified src/category_theory/monad/algebra.lean

modified def category_theory.comonad.adj

added theorem category_theory.comonad.of_left_adjoint_forget

added theorem category_theory.comonad.right_adjoint_forget

added theorem category_theory.monad.left_adjoint_forget

added theorem category_theory.monad.of_right_adjoint_forget

Modified src/category_theory/monad/basic.lean

added def category_theory.comonad_iso.mk

added theorem category_theory.comonad_to_functor_map_iso_comonad_iso_mk

added def category_theory.monad_iso.mk

added theorem category_theory.monad_to_functor_map_iso_monad_iso_mk

Modified src/category_theory/skeletal.lean

Modified src/topology/category/Compactum.lean