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Is the product of two categories with cofibrations still a category with cofibrations?

Suppose I have two $k$-linear categories $\mathcal C$ and $\mathcal D$ which are "categories with cofibrations" (in the Waldhausen sense) Is the product category $\mathcal C\times \mathcal D$ still a ...
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105 views

Could one recover the relative K-theory from the quotient derived category?

Let $A\to B$ be a full embedding of exact categories that induces an embedding $D^b(A)\to D^b(B)$. My question is: what can one say about the relation of the homotopy cofibre $K(A)\to K(B)$ (the ...
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129 views

Split exact categories arising naturally

If you're interested in the $K$-theory of rings, a useful feature of the exact category of finitely generated projective (or free) modules is that it is split exact, i.e. every short exact sequence is ...
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173 views

Given an exact category, viewed as a site, do there exist non-additive sheaves?

Suppose given an exact category $\mathcal{C}$. The following question arises while proving the Gabriel-Quillen-Laumon embedding theorem following Laumon [1]. Laumon constructs an abelian category ...
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60 views

Ex/reg toposes without generic monomorphisms

A generic monomorphism is a monomorphism of which every monomorphisms in the same category is a pullback; it is like a subobject classifier without uniqueness. I am looking for a locally Cartesian ...
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304 views

Quasi-isomorphisms in exact categories

I am trying to understand quasi-isomorphisms in an exact category as defined via the mapping cylinder. I would like to know whether these form a category of weak equivalences in the sense of ...