C∞-algebraic geometry with corners

Introduction
Background on C∞ž-schemes
	Introduction to category theory
	C∞-rings
	Modules and cotangent modules of C∞-rings
	Sheaves
	C∞-schemes
	Complete C∞-rings
	Sheaves of Oₓ-modules on C∞žˆž-ringed spaces
	Sheaves of Oₓ-modules on C∞ˆž-schemes
	Applications of C∞-rings and C∞-schemes
Background on manifolds with (g-)corners
	Manifolds with corners
	Monoids
	Manifolds with g-corners
	Boundaries, corners, and the corner functor
	Tangent bundles and b-tangent bundles
	Applications of manifolds with (g-)corners
(Pre) C∞-rings with corners
	Categorical pre C∞-rings with corners
	Pre C∞-rings with corners
	Adjoints and (co)limits for pre C∞-rings with corners
	C∞-rings with corners
	Generators, relations, and localization
	Local C∞-rings with corners
	Special classes of C∞ˆž-rings with corners
C∞-schemes with corners
	(Local) C∞ˆž-ringed spaces with corners
	Special classes of local C∞ˆž-ringed spaces with corners
	The spectrum functor
	C∞ˆž-schemes with corners
	Semi-complete C∞-rings with corners
	Special classes of C∞ˆž-schemes with corners
	Fibre products of C∞ˆž-schemes with corners
Boundaries, corners, and the corner functor
	The corner functor for C∞-ringed spaces with corners
	The corner functor for C∞-schemes with corners
	The corner functor for firm C∞-schemes with corners
	The sheaves of monoids Mᵉˣ,Mⁱⁿ on C(X)
	The boundary ∂ˆ‚X and k-corners Cᵏ(X)
	Fibre products and corner functors
	B- and c-transverse fibre products in Manᵍᶜⁱⁿ, C∞Schᶜᵗ’ᵒ
Modules, and sheaves of modules
	Modules over C∞-rings with corners, (b-)cotangent modules
	(B-)cotangent modules for manifolds with (g-)corners
	Some computations of b-cotangent modules
	B-cotangent modules of pushouts
	Sheaves of Oₓ-modules, and (b-)cotangent sheaves
	(B-)cotangent sheaves and the corner functor
Further generalizations and applications
	Synthetic Differential Geometry with corners
	C∞-stacks with corners
	C∞ˆž-rings and C∞-schemes with a-corners
	Derived manifolds and orbifolds with corners
Bibliography
Glossary of Notation
Index