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April 30, 2020 17:55
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@eq.{v+1} | |
(@category_theory.has_hom.hom.{v u} C | |
(@category_theory.category_struct.to_has_hom.{v u} C (@category_theory.category.to_category_struct.{v u} C π)) | |
B | |
(@category_theory.exp.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1) | |
A | |
(@sheaf'.A.{v u} C π _inst_1 _inst_2 j _inst_3 s) | |
(@category_theory.is_cartesian_closed.cart_closed.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1) | |
(@category_theory.cc_of_lcc.{v u} C π _inst_1 (@lcc_of_pow.{v u} C π _inst_1 _inst_2)) | |
A))) | |
(@coe_fn.{(max 1 (v+1)) v+1} | |
(equiv.{v+1 v+1} | |
(@category_theory.has_hom.hom.{v u} C | |
(@category_theory.category_struct.to_has_hom.{v u} C | |
(@category_theory.category.to_category_struct.{v u} C π)) | |
(@category_theory.limits.prod.{v u} C π A B | |
(@category_theory.limits.has_limit_of_has_limits_of_shape.{v u} C π | |
(category_theory.discrete.{v} category_theory.limits.walking_pair.{v}) | |
(category_theory.discrete_category.{v} category_theory.limits.walking_pair.{v}) | |
(@category_theory.limits.has_binary_products.has_limits_of_shape.{v u} C π | |
(@category_theory.limits.category_theory.limits.has_binary_products.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1))) | |
(@category_theory.limits.pair.{v u v} C π A B))) | |
(@sheaf'.A.{v u} C π _inst_1 _inst_2 j _inst_3 s)) | |
(@category_theory.has_hom.hom.{v u} C | |
(@category_theory.category_struct.to_has_hom.{v u} C | |
(@category_theory.category.to_category_struct.{v u} C π)) | |
B | |
(@category_theory.exp.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1) | |
A | |
(@sheaf'.A.{v u} C π _inst_1 _inst_2 j _inst_3 s) | |
(@category_theory.is_cartesian_closed.cart_closed.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1) | |
(@category_theory.cc_of_lcc.{v u} C π _inst_1 (@lcc_of_pow.{v u} C π _inst_1 _inst_2)) | |
A)))) | |
(@equiv.has_coe_to_fun.{v+1 v+1} | |
(@category_theory.has_hom.hom.{v u} C | |
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(@category_theory.category.to_category_struct.{v u} C π)) | |
(@category_theory.limits.prod.{v u} C π A B | |
(@category_theory.limits.has_limit_of_has_limits_of_shape.{v u} C π | |
(category_theory.discrete.{v} category_theory.limits.walking_pair.{v}) | |
(category_theory.discrete_category.{v} category_theory.limits.walking_pair.{v}) | |
(@category_theory.limits.has_binary_products.has_limits_of_shape.{v u} C π | |
(@category_theory.limits.category_theory.limits.has_binary_products.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1))) | |
(@category_theory.limits.pair.{v u v} C π A B))) | |
(@sheaf'.A.{v u} C π _inst_1 _inst_2 j _inst_3 s)) | |
(@category_theory.has_hom.hom.{v u} C | |
(@category_theory.category_struct.to_has_hom.{v u} C | |
(@category_theory.category.to_category_struct.{v u} C π)) | |
B | |
(@category_theory.exp.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1) | |
A | |
(@sheaf'.A.{v u} C π _inst_1 _inst_2 j _inst_3 s) | |
(@category_theory.is_cartesian_closed.cart_closed.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1) | |
(@category_theory.cc_of_lcc.{v u} C π _inst_1 (@lcc_of_pow.{v u} C π _inst_1 _inst_2)) | |
A)))) | |
(@category_theory.adjunction.hom_equiv.{v v u u} C π C π | |
(@category_theory.functor.obj.{v (max u v) u (max v u)} C π | |
(@category_theory.functor.{v v u u} C π C π) | |
(@category_theory.functor.category.{v v u u} C π C π) | |
(@category_theory.limits.prod_functor.{v u} C π | |
(@category_theory.limits.category_theory.limits.has_binary_products.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1))) | |
A) | |
(@category_theory.is_left_adjoint.right.{v v u u} C π C π | |
(@category_theory.functor.obj.{v (max u v) u (max v u)} C π | |
(@category_theory.functor.{v v u u} C π C π) | |
(@category_theory.functor.category.{v v u u} C π C π) | |
(@category_theory.limits.prod_functor.{v u} C π | |
(@category_theory.limits.category_theory.limits.has_binary_products.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1))) | |
A) | |
(@category_theory.exponentiable.is_adj.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1) | |
A | |
(@category_theory.is_cartesian_closed.cart_closed.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1) | |
(@category_theory.cc_of_lcc.{v u} C π _inst_1 (@lcc_of_pow.{v u} C π _inst_1 _inst_2)) | |
A))) | |
(@category_theory.is_left_adjoint.adj.{v v u u} C π C π | |
(@category_theory.functor.obj.{v (max u v) u (max v u)} C π | |
(@category_theory.functor.{v v u u} C π C π) | |
(@category_theory.functor.category.{v v u u} C π C π) | |
(@category_theory.limits.prod_functor.{v u} C π | |
(@category_theory.limits.category_theory.limits.has_binary_products.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1))) | |
A) | |
(@category_theory.exponentiable.is_adj.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1) | |
A | |
(@category_theory.is_cartesian_closed.cart_closed.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1) | |
(@category_theory.cc_of_lcc.{v u} C π _inst_1 (@lcc_of_pow.{v u} C π _inst_1 _inst_2)) | |
A))) | |
B | |
(@sheaf'.A.{v u} C π _inst_1 _inst_2 j _inst_3 s)) | |
(@coe_fn.{(max 1 (v+1)) v+1} | |
(equiv.{v+1 v+1} | |
(@category_theory.has_hom.hom.{v u} C | |
(@category_theory.category_struct.to_has_hom.{v u} C | |
(@category_theory.category.to_category_struct.{v u} C π)) | |
B | |
(@category_theory.exp.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1) | |
A | |
(@sheaf'.A.{v u} C π _inst_1 _inst_2 j _inst_3 s) | |
(@category_theory.is_cartesian_closed.cart_closed.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1) | |
(@category_theory.cc_of_lcc.{v u} C π _inst_1 (@lcc_of_pow.{v u} C π _inst_1 _inst_2)) | |
A))) | |
(@category_theory.has_hom.hom.{v u} C | |
(@category_theory.category_struct.to_has_hom.{v u} C | |
(@category_theory.category.to_category_struct.{v u} C π)) | |
(@category_theory.limits.prod.{v u} C π A B | |
(@category_theory.limits.has_limit_of_has_limits_of_shape.{v u} C π | |
(category_theory.discrete.{v} category_theory.limits.walking_pair.{v}) | |
(category_theory.discrete_category.{v} category_theory.limits.walking_pair.{v}) | |
(@category_theory.limits.has_binary_products.has_limits_of_shape.{v u} C π | |
(@category_theory.limits.category_theory.limits.has_binary_products.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1))) | |
(@category_theory.limits.pair.{v u v} C π A B))) | |
(@sheaf'.A.{v u} C π _inst_1 _inst_2 j _inst_3 s))) | |
(@equiv.has_coe_to_fun.{v+1 v+1} | |
(@category_theory.has_hom.hom.{v u} C | |
(@category_theory.category_struct.to_has_hom.{v u} C | |
(@category_theory.category.to_category_struct.{v u} C π)) | |
B | |
(@category_theory.exp.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1) | |
A | |
(@sheaf'.A.{v u} C π _inst_1 _inst_2 j _inst_3 s) | |
(@category_theory.is_cartesian_closed.cart_closed.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1) | |
(@category_theory.cc_of_lcc.{v u} C π _inst_1 (@lcc_of_pow.{v u} C π _inst_1 _inst_2)) | |
A))) | |
(@category_theory.has_hom.hom.{v u} C | |
(@category_theory.category_struct.to_has_hom.{v u} C | |
(@category_theory.category.to_category_struct.{v u} C π)) | |
(@category_theory.limits.prod.{v u} C π A B | |
(@category_theory.limits.has_limit_of_has_limits_of_shape.{v u} C π | |
(category_theory.discrete.{v} category_theory.limits.walking_pair.{v}) | |
(category_theory.discrete_category.{v} category_theory.limits.walking_pair.{v}) | |
(@category_theory.limits.has_binary_products.has_limits_of_shape.{v u} C π | |
(@category_theory.limits.category_theory.limits.has_binary_products.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1))) | |
(@category_theory.limits.pair.{v u v} C π A B))) | |
(@sheaf'.A.{v u} C π _inst_1 _inst_2 j _inst_3 s))) | |
(@equiv.symm.{v+1 v+1} | |
(@category_theory.has_hom.hom.{v u} C | |
(@category_theory.category_struct.to_has_hom.{v u} C | |
(@category_theory.category.to_category_struct.{v u} C π)) | |
(@category_theory.limits.prod.{v u} C π A B | |
(@category_theory.limits.has_limit_of_has_limits_of_shape.{v u} C π | |
(category_theory.discrete.{v} category_theory.limits.walking_pair.{v}) | |
(category_theory.discrete_category.{v} category_theory.limits.walking_pair.{v}) | |
(@category_theory.limits.has_binary_products.has_limits_of_shape.{v u} C π | |
(@category_theory.limits.category_theory.limits.has_binary_products.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1))) | |
(@category_theory.limits.pair.{v u v} C π A B))) | |
(@sheaf'.A.{v u} C π _inst_1 _inst_2 j _inst_3 s)) | |
(@category_theory.has_hom.hom.{v u} C | |
(@category_theory.category_struct.to_has_hom.{v u} C | |
(@category_theory.category.to_category_struct.{v u} C π)) | |
B | |
(@category_theory.exp.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1) | |
A | |
(@sheaf'.A.{v u} C π _inst_1 _inst_2 j _inst_3 s) | |
(@category_theory.is_cartesian_closed.cart_closed.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1) | |
(@category_theory.cc_of_lcc.{v u} C π _inst_1 (@lcc_of_pow.{v u} C π _inst_1 _inst_2)) | |
A))) | |
(@category_theory.adjunction.hom_equiv.{v v u u} C π C π | |
(@category_theory.functor.obj.{v (max u v) u (max v u)} C π | |
(@category_theory.functor.{v v u u} C π C π) | |
(@category_theory.functor.category.{v v u u} C π C π) | |
(@category_theory.limits.prod_functor.{v u} C π | |
(@category_theory.limits.category_theory.limits.has_binary_products.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1))) | |
A) | |
(@category_theory.is_left_adjoint.right.{v v u u} C π C π | |
(@category_theory.functor.obj.{v (max u v) u (max v u)} C π | |
(@category_theory.functor.{v v u u} C π C π) | |
(@category_theory.functor.category.{v v u u} C π C π) | |
(@category_theory.limits.prod_functor.{v u} C π | |
(@category_theory.limits.category_theory.limits.has_binary_products.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1))) | |
A) | |
(@category_theory.exponentiable.is_adj.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1) | |
A | |
(@category_theory.is_cartesian_closed.cart_closed.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1) | |
(@category_theory.cc_of_lcc.{v u} C π _inst_1 (@lcc_of_pow.{v u} C π _inst_1 _inst_2)) | |
A))) | |
(@category_theory.is_left_adjoint.adj.{v v u u} C π C π | |
(@category_theory.functor.obj.{v (max u v) u (max v u)} C π | |
(@category_theory.functor.{v v u u} C π C π) | |
(@category_theory.functor.category.{v v u u} C π C π) | |
(@category_theory.limits.prod_functor.{v u} C π | |
(@category_theory.limits.category_theory.limits.has_binary_products.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1))) | |
A) | |
(@category_theory.exponentiable.is_adj.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1) | |
A | |
(@category_theory.is_cartesian_closed.cart_closed.{v u} C π | |
(@category_theory.limits.has_finite_products_of_has_finite_limits.{v u} C π _inst_1) | |
(@category_theory.cc_of_lcc.{v u} C π _inst_1 (@lcc_of_pow.{v u} C π _inst_1 _inst_2)) | |
A))) | |
B | |
(@sheaf'.A.{v u} C π _inst_1 _inst_2 j _inst_3 s))) | |
a)) | |
a |
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