We prove the Hurewicz theorem in homotopy type theory, i.e., that for $X$ a pointed, $(n-1)$-connected $(n \geq 1)$ and $A$ an abelian group, there is natural isomorphism $\pi_n(X)^{ab} \otimes A \cong \tilde{H}_n(X; A)$ relating abelianization of groups with homology. also compute connectivity smash product types express lowest non-trivial group as tensor product. Along way, we study magmas, l...

We prove a constructive existence theorem for abelian envelopes of non-abelian monoidal categories. This establishes new tool the construction tensor As an example we obtain proofs several universal categories as conjectured by Deligne. Another constructs interesting in positive characteristic via tilting modules ${\rm SL}_2$ .

When an antisymmetric tensor potential is coupled to the field strength of a gauge field via a B∧F coupling and a kinetic term for B is included, the gauge field develops an effective mass. The theory can be made invariant under a non-abelian vector gauge symmetry by introducing an auxiliary vector field. The covariant quantization of this theory requires ghosts for ghosts. The resultant theory...

The object of this paper is to prove that the standard categories in which homotopy theory is done, such as topological spaces, simplicial sets, chain complexes of abelian groups, and any of the various good models for spectra, are all homotopically self-contained. The left half of this statement essentially means that any functor that looks like it could be a tensor product (or product, or sma...

It is well known in the work of Kadison and Ringrose 1983 that if A and B are maximal abelian von Neumann subalgebras of von Neumann algebras M and N, respectively, then A⊗B is a maximal abelian von Neumann subalgebra of M⊗N. It is then natural to ask whether a similar result holds in the context of JW-algebras and the JW-tensor product. Guided to some extent by the close relationship between a...

A systematic method is presented for the construction and classification of algebras gauge transformations arbitrary high rank tensor fields. For every field a given rank, transformation will be stated, in generic way, via an ansatz that contains all possible terms, with coefficients maximum number functions. The requirement closure algebra prove to restrictive, but, nevertheless, leave variety...