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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.

7 votes

From chain complex to simplicial abelian group

This is the Dold-Kan correspondence.
Robin Chapman's user avatar
3 votes
Accepted

Finite categories and partial orders

Almost, this has nothing to do with finiteness: any category where the homsets have at most one element each is a preorder. Define $a\le b$ if there is an arrow from $a$ to $b$. Then $\le$ is reflexiv …
Robin Chapman's user avatar
7 votes
2 answers
2k views

Describing global sections of sheafifications

Recently on glancing through Hartshorne's description of Cartier divisors I started pondering the definition of sheafification which led me to a question I can't answer. Neither can I find a discussio …
1 vote

Can all induced maps be described categorically.?. (or at least as generally as possible)

The key word in this context is functor. The point is that homology, homotopy etc. are functors. For example consider homology $H_n$. This is a functor from the category of topological spaces to the c …
Robin Chapman's user avatar
7 votes

why haven't certain well-researched classes of mathematical object been framed by category t...

Paul Taylor's "Abstract Stone Duality" http://www.paultaylor.eu/ASD/ is an attempt to recast elementary real analysis (including sequences) involving categorical ideas.
Robin Chapman's user avatar
17 votes
Accepted

What is an antiequivalence of two categories?

All it means that one of the categories is equivalent to the opposite of the other. Wikipedia has informative pages on opposites of categories and equivalences of categories: http://en.wikipedia.org …
Robin Chapman's user avatar