Type theory and homotopy theory have evolved into profoundly interconnected disciplines. Type theory, with its foundations in logic and computer science, provides a formal language for constructing ...

Various aspects of homotopy theory in the category of simplicial spaces are developed. Topics covered include continuous cohomology, continuous de Rham cohomology, the Kan extension condition, the ...

Abstract: The ?-category Cond(Ani) of condensed anima combines the homotopy-theoretic direction of anima with the topological space direction of condensed sets. For example, we can recover the shape ...

We prove that the space B0 U(1) of equivalence classes of U(1)-invariant connections on some SU(2)-principle bundles over S4 is weakly homotopy equivalent to a component of the second loop space Ω2(S2 ...

Abstract: The Hermitian K-theory of a ring or scheme is a variant of algebraic K-theory in which we use vector bundles equipped with a non-degenerate symmetric bilinear form. From the perspective of ...

« Mike Otsuka (LSE): How it makes a moral difference that one is worse off than one would have been ...

Cobordism theory, a cornerstone of geometric topology, analyses the equivalence classes of manifolds by utilising the concept of cobordism – whereby two manifolds are considered equivalent if they ...